Electrostatics involves electric charges, the forces between … · 2013-03-25 · 32...
Transcript of Electrostatics involves electric charges, the forces between … · 2013-03-25 · 32...
32 Electrostatics
Electrostatics involves
electric charges, the forces
between them, and their
behavior in materials.
32 Electrostatics
Electrostatics, or electricity at rest, involves electric charges, the forces between them, and their behavior in materials. An understanding of electricity requires a step-by-step approach, for one concept is the building block for the next.
32 Electrostatics
The fundamental rule at the base of all electrical
phenomena is that like charges repel and opposite
charges attract.
32.1 Electrical Forces and Charges
32 Electrostatics
Consider a force acting on you that is billions upon
billions of times stronger than gravity.
Suppose that in addition to this enormous force
there is a repelling force, also billions upon billions
of times stronger than gravity.
The two forces acting on you would balance each
other and have no noticeable effect at all.
A pair of such forces acts on you all the time—
electrical forces.
32.1 Electrical Forces and Charges
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The enormous attractive and
repulsive electrical forces
between the charges in Earth
and the charges in your body
balance out, leaving the relatively
weaker force of gravity, which
only attracts.
32.1 Electrical Forces and Charges
32 Electrostatics
The Atom
Electrical forces arise from particles in atoms.
The protons in the nucleus attract the electrons and hold them
in orbit. Electrons are attracted to protons, but electrons repel
other electrons.
32.1 Electrical Forces and Charges
32 Electrostatics
The fundamental electrical property to which the
mutual attractions or repulsions between electrons
or protons is attributed is called charge.
By convention, electrons are negatively charged
and protons positively charged.
Neutrons have no charge, and are neither attracted
nor repelled by charged particles.
32.1 Electrical Forces and Charges
32 Electrostatics
The helium nucleus is composed of two protons and
two neutrons. The positively charged protons attract
two negative electrons.
32.1 Electrical Forces and Charges
32 Electrostatics
Here are some important facts about atoms:
• Every atom has a positively charged nucleus
surrounded by negatively charged electrons.
• All electrons are identical.
• The nucleus is composed of protons and neutrons. All
protons are identical; similarly, all neutrons are identical.
• Atoms usually have as many electrons as protons, so
the atom has zero net charge.
A proton has nearly 2000 times the mass of an electron, but
its positive charge is equal in magnitude to the negative
charge of the electron.
32.1 Electrical Forces and Charges
32 Electrostatics
Attraction and Repulsion
32.1 Electrical Forces and Charges
32 Electrostatics
The fundamental rule of all
electrical phenomena is that
like charges repel and
opposite charges attract.
32.1 Electrical Forces and Charges
32 Electrostatics
What is the fundamental rule at the base of all
electrical phenomena?
32.1 Electrical Forces and Charges
32 Electrostatics
An object that has unequal numbers of electrons
and protons is electrically charged.
32.2 Conservation of Charge
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Electrons and protons have electric charge.
In a neutral atom, there are as many electrons as protons, so
there is no net charge.
32.2 Conservation of Charge
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If an electron is removed from an atom, the atom is
no longer neutral. It has one more positive charge
than negative charge.
A charged atom is called an ion.
• A positive ion has a net positive charge; it has
lost one or more electrons.
• A negative ion has a net negative charge; it has
gained one or more extra electrons.
32.2 Conservation of Charge
32 Electrostatics
Electrically Charged Objects
Matter is made of atoms, and atoms are made of
electrons and protons.
An object that has equal numbers of electrons
and protons has no net electric charge.
But if there is an imbalance in the numbers, the
object is then electrically charged.
An imbalance comes about by adding or
removing electrons.
32.2 Conservation of Charge
32 Electrostatics
The innermost electrons in an atom are bound very tightly to
the oppositely charged atomic nucleus.
The outermost electrons of many atoms are bound very
loosely and can be easily dislodged.
How much energy is required to tear an electron away from
an atom varies for different substances.
32.2 Conservation of Charge
32 Electrostatics
When electrons are transferred
from the fur to the rod, the rod
becomes negatively charged.
32.2 Conservation of Charge
32 Electrostatics
Principle of Conservation of Charge
Electrons are neither created nor
destroyed but are simply
transferred from one material to
another. This principle is known as
conservation of charge.
In every event, whether large-scale
or at the atomic and nuclear level,
the principle of conservation of
charge applies.
32.2 Conservation of Charge
32 Electrostatics
Any object that is electrically charged has an excess or
deficiency of some whole number of electrons—electrons
cannot be divided into fractions of electrons.
This means that the charge of the object is a whole-number
multiple of the charge of an electron.
32.2 Conservation of Charge
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think!
If you scuff electrons onto your shoes while walking across
a rug, are you negatively or positively charged?
32.2 Conservation of Charge
32 Electrostatics
think!
If you scuff electrons onto your shoes while walking across
a rug, are you negatively or positively charged?
Answer:
When your rubber- or plastic-soled shoes drag across the
rug, they pick up electrons from the rug in the same way
you charge a rubber or plastic rod by rubbing it with a cloth.
You have more electrons after you scuff your shoes, so you
are negatively charged (and the rug is positively charged).
32.2 Conservation of Charge
32 Electrostatics
What causes an object to become
electrically charged?
32.2 Conservation of Charge
32 Electrostatics
Coulomb’s law states that for charged particles or
objects that are small compared with the distance
between them, the force between the charges varies
directly as the product of the charges and inversely
as the square of the distance between them.
32.3 Coulomb’s Law
32 Electrostatics
Recall from Newton’s law of gravitation that the gravitational
force between two objects of mass m1 and mass m2 is
proportional to the product of the masses and inversely
proportional to the square of the distance d between them:
32.3 Coulomb’s Law
32 Electrostatics
Force, Charges, and Distance
The electrical force between any two objects obeys a similar
inverse-square relationship with distance.
The relationship among electrical force, charges, and
distance—Coulomb’s law—was discovered by the French
physicist Charles Coulomb in the eighteenth century.
32.3 Coulomb’s Law
32 Electrostatics
For charged objects, the force between the charges varies
directly as the product of the charges and inversely as the
square of the distance between them.
Where:
d is the distance between the charged particles.
q1 represents the quantity of charge of one particle.
q2 is the quantity of charge of the other particle.
k is the proportionality constant.
32.3 Coulomb’s Law
32 Electrostatics
The SI unit of charge is the coulomb, abbreviated C.
A charge of 1 C is the charge of 6.24 × 1018 electrons.
A coulomb represents the amount of charge that passes
through a common 100-W light bulb in about one second.
32.3 Coulomb’s Law
32 Electrostatics
The Electrical Proportionality Constant
The proportionality constant k in Coulomb’s law is similar to G
in Newton’s law of gravitation.
k = 9,000,000,000 N·m2/C2 or 9.0 × 109 N·m2/C2
If a pair of charges of 1 C each were 1 m apart, the force of
repulsion between the two charges would be
9 billion newtons.
That would be more than 10 times the weight of a battleship!
32.3 Coulomb’s Law
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Newton’s law of gravitation for masses is similar to Coulomb’s law for
electric charges.
Whereas the gravitational force of attraction between a pair of one-
kilogram masses is extremely small, the electrical force between a pair of
one-coulomb charges is extremely large.
The greatest difference between gravitation and electrical forces is that
gravity only attracts but electrical forces may attract or repel.
32.3 Coulomb’s Law
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Electrical Forces in Atoms
Because most objects have almost exactly equal numbers of
electrons and protons, electrical forces usually balance out.
Between Earth and the moon, for example, there is no
measurable electrical force.
In general, the weak gravitational force, which only attracts, is
the predominant force between astronomical bodies.
32.3 Coulomb’s Law
32 Electrostatics
Although electrical forces balance out for
astronomical and everyday objects, at the atomic
level this is not always true.
Often two or more atoms, when close together,
share electrons.
Bonding results when the attractive force between
the electrons of one atom and the positive nucleus
of another atom is greater than the repulsive force
between the electrons of both atoms. Bonding leads
to the formation of molecules.
32.3 Coulomb’s Law
32 Electrostatics
think!
What is the chief significance of the fact that G in Newton’s
law of gravitation is a small number and k in Coulomb’s law
is a large number when both are expressed in SI units?
32.3 Coulomb’s Law
32 Electrostatics
think!
What is the chief significance of the fact that G in Newton’s
law of gravitation is a small number and k in Coulomb’s law
is a large number when both are expressed in SI units?
Answer:
The small value of G indicates that gravity is a weak force;
the large value of k indicates that the electrical force is
enormous in comparison.
32.3 Coulomb’s Law
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think!
a. If an electron at a certain distance from a charged particle
is attracted with a certain force, how will the force compare
at twice this distance?
32.3 Coulomb’s Law
32 Electrostatics
think!
a. If an electron at a certain distance from a charged particle
is attracted with a certain force, how will the force compare
at twice this distance?
Answer:
a. In accord with the inverse-square law, at twice the
distance the force will be one fourth as much.
32.3 Coulomb’s Law
32 Electrostatics
think!
a. If an electron at a certain distance from a charged particle
is attracted with a certain force, how will the force compare
at twice this distance?
b. Is the charged particle in this case positive or negative?
Answer:
a. In accord with the inverse-square law, at twice the
distance the force will be one fourth as much.
32.3 Coulomb’s Law
32 Electrostatics
think!
a. If an electron at a certain distance from a charged particle
is attracted with a certain force, how will the force compare
at twice this distance?
b. Is the charged particle in this case positive or negative?
Answer:
a. In accord with the inverse-square law, at twice the
distance the force will be one fourth as much.
b. Since there is a force of attraction, the charges must be
opposite in sign, so the charged particle is positive.
32.3 Coulomb’s Law
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What does Coulomb’s law state?
32.3 Coulomb’s Law
32 Electrostatics
Electrons move easily in good conductors and
poorly in good insulators.
32.4 Conductors and Insulators
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Outer electrons of the atoms in a metal are not
anchored to the nuclei of particular atoms, but are
free to roam in the material.
Materials through which electric charge can flow are
called conductors.
Metals are good conductors for the motion of
electric charges because their electrons are “loose.”
32.4 Conductors and Insulators
32 Electrostatics
Electrons in other materials—rubber and glass, for
example—are tightly bound and remain with
particular atoms.
They are not free to wander about to other atoms in
the material.
These materials, known as insulators, are poor
conductors of electricity.
32.4 Conductors and Insulators
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A substance is classified as a
conductor or an insulator based on
how tightly the atoms of the
substance hold their electrons.
The conductivity of a metal can be
more than a million trillion times
greater than the conductivity of an
insulator such as glass.
In power lines, charge flows much
more easily through hundreds of
kilometers of metal wire than through
the few centimeters of insulating
material that separates the wire from
the supporting tower.
32.4 Conductors and Insulators
32 Electrostatics
Semiconductors are materials that can be made to behave
sometimes as insulators and sometimes as conductors.
Atoms in a semiconductor hold their electrons until given
small energy boosts.
This occurs in photovoltaic cells that convert solar energy
into electrical energy.
Thin layers of semiconducting materials sandwiched
together make up transistors.
32.4 Conductors and Insulators
32 Electrostatics
What is the difference between a good
conductor and a good insulator?
32.4 Conductors and Insulators
32 Electrostatics
Two ways electric charge can be transferred are by
friction and by contact.
32.5 Charging by Friction and Contact
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We can stroke a cat’s fur and hear the crackle of sparks that
are produced.
We can comb our hair in front of a mirror in a dark room and
see as well as hear the sparks of electricity.
We can scuff our shoes across a rug and feel the tingle as
we reach for the doorknob.
Electrons are being transferred by friction when one
material rubs against another.
32.5 Charging by Friction and Contact
32 Electrostatics
If you slide across a seat in an automobile, you are in
danger of being charged by friction.
32.5 Charging by Friction and Contact
32 Electrostatics
Electrons can also be transferred from one material to another
by simply touching.
When a charged rod is placed in contact with a neutral object,
some charge will transfer to the neutral object.
This method of charging is called charging by contact.
If the object is a good conductor, the charge will spread to all
parts of its surface because the like charges repel each other.
32.5 Charging by Friction and Contact
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What are two ways electric charge can
be transferred?
32.5 Charging by Friction and Contact
32 Electrostatics
If a charged object is brought near a conducting
surface, even without physical contact, electrons
will move in the conducting surface.
32.6 Charging by Induction
32 Electrostatics
Charging by induction can be illustrated using two insulated
metal spheres.
Uncharged insulated metal spheres touching each other, in
effect, form a single noncharged conductor.
32.6 Charging by Induction
32 Electrostatics
• When a negatively charged rod is held near one sphere, electrons in the
metal are repelled by the rod.
• Excess negative charge has moved to the other sphere, leaving the first
sphere with an excess positive charge.
• The charge on the spheres has been redistributed, or induced.
32.6 Charging by Induction
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• When the spheres are separated and the rod removed, the spheres are
charged equally and oppositely.
• They have been charged by induction, which is the charging of an
object without direct contact.
32.6 Charging by Induction
32 Electrostatics
Charge induction by grounding can be illustrated using a metal sphere hanging from
a nonconducting string.
32.6 Charging by Induction
32 Electrostatics
Charge induction by grounding can be illustrated using a metal sphere hanging from
a nonconducting string.
• A charge redistribution is induced by the presence of the charged rod. The
net charge on the sphere is still zero.
32.6 Charging by Induction
32 Electrostatics
Charge induction by grounding can be illustrated using a metal sphere hanging from
a nonconducting string.
• A charge redistribution is induced by the presence of the charged rod. The
net charge on the sphere is still zero.
• Touching the sphere removes electrons by contact and the sphere is left
positively charged.
32.6 Charging by Induction
32 Electrostatics
Charge induction by grounding can be illustrated using a metal sphere hanging from
a nonconducting string.
• A charge redistribution is induced by the presence of the charged rod. The
net charge on the sphere is still zero.
• Touching the sphere removes electrons by contact and the sphere is left
positively charged.
• The positively charged sphere is attracted to a negative rod.
32.6 Charging by Induction
32 Electrostatics
Charge induction by grounding can be illustrated using a metal sphere hanging from
a nonconducting string.
• A charge redistribution is induced by the presence of the charged rod. The
net charge on the sphere is still zero.
• Touching the sphere removes electrons by contact and the sphere is left
positively charged.
• The positively charged sphere is attracted to a negative rod.
• When electrons move onto the sphere from the rod, it becomes negatively
charged by contact.
32.6 Charging by Induction
32 Electrostatics
When we touch the metal surface with a finger, charges that
repel each other have a conducting path to a practically infinite
reservoir for electric charge—the ground.
When we allow charges to move off (or onto) a conductor by
touching it, we are grounding it.
32.6 Charging by Induction
32 Electrostatics
Charging by induction occurs during
thunderstorms.
The negatively charged bottoms of
clouds induce a positive charge on the
surface of Earth below.
Most lightning is an electrical
discharge between oppositely charged
parts of clouds.
The kind of lightning we are most
familiar with is the electrical discharge
between clouds and oppositely
charged ground below.
32.6 Charging by Induction
32 Electrostatics
If a rod is placed above a building and connected to the
ground, the point of the rod collects electrons from the air.
This prevents a buildup of positive charge by induction.
The primary purpose of the lightning rod is to prevent a
lightning discharge from occurring.
If lightning does strike, it may be attracted to the rod and short-
circuited to the ground, sparing the building.
32.6 Charging by Induction
32 Electrostatics
think!
Why does the negative rod in the two-sphere example have
the same charge before and after the spheres are charged, but
not when charging takes place in the single-sphere example?
32.6 Charging by Induction
32 Electrostatics
think!
Why does the negative rod in the two-sphere example have
the same charge before and after the spheres are charged, but
not when charging takes place in the single-sphere example?
Answer:
In the first charging process, no contact was made between
the negative rod and either of the spheres. In the second
charging process, however, the rod touched the sphere when
it was positively charged. A transfer of charge by contact
reduced the negative charge on the rod.
32.6 Charging by Induction
32 Electrostatics
What happens when a charged object is
placed near a conducting surface?
32.6 Charging by Induction
32 Electrostatics
Charge polarization can occur in insulators that are
near a charged object.
32.7 Charge Polarization
32 Electrostatics
Charging by induction is not restricted to conductors.
Charge polarization can occur in insulators that are
near a charged object.
When a charged rod is brought near an insulator, there
are no free electrons to migrate throughout the
insulating material.
Instead, there is a rearrangement of the positions of
charges within the atoms and molecules themselves.
32.7 Charge Polarization
32 Electrostatics
One side of the atom or molecule is induced to be slightly
more positive (or negative) than the opposite side.
The atom or molecule is said to be electrically polarized.
32.7 Charge Polarization
32 Electrostatics
a. When an external negative charge is brought closer
from the left, the charges within a neutral atom or
molecule rearrange.
32.7 Charge Polarization
32 Electrostatics
a. When an external negative charge is brought closer
from the left, the charges within a neutral atom or
molecule rearrange.
b. All the atoms or molecules near the surface of the
insulator become electrically polarized.
32.7 Charge Polarization
32 Electrostatics
Examples of Charge Polarization
Polarization explains why electrically neutral bits of paper are
attracted to a charged object, such as a charged comb.
Molecules are polarized in the paper, with the oppositely
charged sides of molecules closest to the charged object.
32.7 Charge Polarization
32 Electrostatics
The bits of paper experience a net attraction.
Sometimes they will cling to the charged object and
suddenly fly off.
Charging by contact has occurred; the paper bits have
acquired the same sign of charge as the charged object
and are then repelled.
32.7 Charge Polarization
32 Electrostatics
A charged comb attracts an uncharged piece of paper
because the force of attraction for the closer charge is
greater than the force of repulsion for the farther charge.
32.7 Charge Polarization
32 Electrostatics
Rub an inflated balloon on your hair and it becomes charged.
Place the balloon against the wall and it sticks.
The charge on the balloon induces an opposite surface charge
on the wall. The charge on the balloon is slightly closer to the
opposite induced charge than to the charge of the same sign.
32.7 Charge Polarization
32 Electrostatics
Electric Dipoles
Many molecules—H2O, for
example—are electrically
polarized in their normal states.
The distribution of electric
charge is not perfectly even.
There is a little more negative
charge on one side of the
molecule than on the other.
Such molecules are said to be
electric dipoles.
32.7 Charge Polarization
32 Electrostatics
32.7 Charge Polarization
32 Electrostatics
In summary, objects are electrically charged in three ways.
• By friction, when electrons are transferred by friction from
one object to another.
• By contact, when electrons are transferred from one
object to another by direct contact without rubbing.
• By induction, when electrons are caused to gather or
disperse by the presence of nearby charge without
physical contact.
32.7 Charge Polarization
32 Electrostatics
If the object is an insulator, on the other hand, then a
realignment of charge rather than a migration of
charge occurs.
This is charge polarization, in which the surface near
the charged object becomes oppositely charged.
32.7 Charge Polarization
32 Electrostatics
What happens when an insulator is in the
presence of a charged object?
32.7 Charge Polarization
32 Electrostatics
1. If a neutral atom has 22 protons in its nucleus, the number of
surrounding electrons is
a. less than 22.
b. 22.
c. more than 22.
d. unknown.
Assessment Questions
32 Electrostatics
1. If a neutral atom has 22 protons in its nucleus, the number of
surrounding electrons is
a. less than 22.
b. 22.
c. more than 22.
d. unknown.
Answer: B
Assessment Questions
32 Electrostatics
2. When we say charge is conserved, we mean that charge can
a. be saved, like money in a bank.
b. only be transferred from one place to another.
c. take equivalent forms.
d. be created or destroyed, as in nuclear reactions.
Assessment Questions
32 Electrostatics
2. When we say charge is conserved, we mean that charge can
a. be saved, like money in a bank.
b. only be transferred from one place to another.
c. take equivalent forms.
d. be created or destroyed, as in nuclear reactions.
Answer: B
Assessment Questions
32 Electrostatics
3. A difference between Newton’s law of gravity and Coulomb’s law is
that only one of these
a. is a fundamental physical law.
b. uses a proportionality constant.
c. invokes the inverse-square law.
d. involves repulsive as well as attractive forces.
Assessment Questions
32 Electrostatics
3. A difference between Newton’s law of gravity and Coulomb’s law is
that only one of these
a. is a fundamental physical law.
b. uses a proportionality constant.
c. invokes the inverse-square law.
d. involves repulsive as well as attractive forces.
Answer: D
Assessment Questions
32 Electrostatics
4. Which is the predominant carrier of charge in copper wire?
a. protons
b. electrons
c. ions
d. neutrons
Assessment Questions
32 Electrostatics
4. Which is the predominant carrier of charge in copper wire?
a. protons
b. electrons
c. ions
d. neutrons
Answer: B
Assessment Questions
32 Electrostatics
5. When you scuff electrons off a rug with your shoes, your shoes
are then
a. negatively charged.
b. positively charged.
c. ionic.
d. electrically neutral.
Assessment Questions
32 Electrostatics
5. When you scuff electrons off a rug with your shoes, your shoes
are then
a. negatively charged.
b. positively charged.
c. ionic.
d. electrically neutral.
Answer: A
Assessment Questions
32 Electrostatics
6. When a cloud that is negatively charged on its bottom and
positively charged on its top moves over the ground below, the
ground acquires
a. a negative charge.
b. a positive charge.
c. no charge since the cloud is electrically neutral.
d. an electrically grounded state.
Assessment Questions
32 Electrostatics
6. When a cloud that is negatively charged on its bottom and
positively charged on its top moves over the ground below, the
ground acquires
a. a negative charge.
b. a positive charge.
c. no charge since the cloud is electrically neutral.
d. an electrically grounded state.
Answer: B
Assessment Questions
32 Electrostatics
7. When a negatively charged balloon is placed against a non-
conducting wall, positive charges in the wall are
a. attracted to the balloon.
b. repelled from the balloon.
c. too bound to negative charges in the wall to have any effect.
d. neutralized.
Assessment Questions
32 Electrostatics
7. When a negatively charged balloon is placed against a non-
conducting wall, positive charges in the wall are
a. attracted to the balloon.
b. repelled from the balloon.
c. too bound to negative charges in the wall to have any effect.
d. neutralized.
Answer: A
Assessment Questions
33 Electric Fields and Potential
An electric field is a
storehouse of energy.
33 Electric Fields and Potential
The space around a concentration of electric charge is different from how it would be if the charge were not there. If you walk by the charged dome of an electrostatic machine—a Van de Graaff generator, for example—you can sense the charge. Hair on your body stands out—just a tiny bit if you’re more than a meter away, and more if you’re closer. The space is said to contain a force field.
33 Electric Fields and Potential
The magnitude (strength) of an electric field can be
measured by its effect on charges located in the
field. The direction of an electric field at any point,
by convention, is the direction of the electrical force
on a small positive test charge placed at that point.
33.1 Electric Fields
33 Electric Fields and Potential
If you throw a ball upward, it follows a curved path
due to interaction between the centers of gravity of
the ball and Earth.
The centers of gravity are far apart, so this is “action
at a distance.”
The concept of a force field explains how Earth can
exert a force on things without touching them.
The ball is in contact with the field all the time.
33.1 Electric Fields
33 Electric Fields and Potential
You can sense the force field that surrounds a
charged Van de Graaff generator.
33.1 Electric Fields
33 Electric Fields and Potential
An electric field is a force field that surrounds an electric charge or group
of charges.
33.1 Electric Fields
33 Electric Fields and Potential
An electric field is a force field that surrounds an electric charge or group
of charges.
A gravitational force holds a satellite in orbit about a planet, and an electrical force holds an electron in orbit about a proton.
33.1 Electric Fields
33 Electric Fields and Potential
An electric field is a force field that surrounds an electric charge or group
of charges.
A gravitational force holds a satellite in orbit about a planet, and an electrical force holds an electron in orbit about a proton.
The force that one electric charge exerts on another is the interaction
between one charge and the electric field of the other.
33.1 Electric Fields
33 Electric Fields and Potential
An electric field has both magnitude and direction. The
magnitude can be measured by its effect on charges
located in the field.
Imagine a small positive “test charge” placed in an
electric field.
• Where the force is greatest on the test charge, the
field is strongest.
• Where the force on the test charge is weak, the
field is small.
33.1 Electric Fields
33 Electric Fields and Potential
The direction of an electric field at any point, by
convention, is the direction of the electrical force on a
small positive test charge.
• If the charge that sets up the field is positive, the
field points away from that charge.
• If the charge that sets up the field is negative, the
field points toward that charge.
33.1 Electric Fields
33 Electric Fields and Potential
How are the magnitude and direction of an
electric field determined?
33.1 Electric Fields
33 Electric Fields and Potential
You can use electric field lines (also called lines of
force) to represent an electric field. Where the lines
are farther apart, the field is weaker.
33.2 Electric Field Lines
33 Electric Fields and Potential
Since an electric field has both magnitude and direction, it is a
vector quantity and can be represented by vectors.
• A negatively charged particle is surrounded by vectors
that point toward the particle.
• For a positively charged particle, the vectors point away.
• Magnitude of the field is indicated by the vector length.
The electric field is greater where the vectors are longer.
33.2 Electric Field Lines
33 Electric Fields and Potential
You can use electric field lines to represent an electric field.
• Where the lines are farther apart, the field is weaker.
• For an isolated charge, the lines extend to infinity.
• For two or more opposite charges, the lines emanate
from a positive charge and terminate on a
negative charge.
33.2 Electric Field Lines
33 Electric Fields and Potential
a. In a vector representation of
an electric field, the length of
the vectors indicates the
magnitude of the field.
33.2 Electric Field Lines
33 Electric Fields and Potential
a. In a vector representation of
an electric field, the length of
the vectors indicates the
magnitude of the field.
b. In a lines-of-force
representation, the distance
between field lines indicates
magnitudes.
33.2 Electric Field Lines
33 Electric Fields and Potential
a. The field lines around a single positive charge extend to infinity.
33.2 Electric Field Lines
33 Electric Fields and Potential
a. The field lines around a single positive charge extend to infinity.
b. For a pair of equal but opposite charges, the field lines emanate
from the positive charge and terminate on the negative charge.
33.2 Electric Field Lines
33 Electric Fields and Potential
a. The field lines around a single positive charge extend to infinity.
b. For a pair of equal but opposite charges, the field lines emanate
from the positive charge and terminate on the negative charge.
c. Field lines are evenly spaced between two oppositely charged
capacitor plates.
33.2 Electric Field Lines
33 Electric Fields and Potential
You can demonstrate electric field patterns
by suspending fine thread in an oil bath with
charged conductors. The photos show
patterns for
a. equal and opposite charges;
33.2 Electric Field Lines
33 Electric Fields and Potential
You can demonstrate electric field patterns
by suspending fine thread in an oil bath with
charged conductors. The photos show
patterns for
a. equal and opposite charges;
b. equal like charges;
33.2 Electric Field Lines
33 Electric Fields and Potential
You can demonstrate electric field patterns
by suspending fine thread in an oil bath with
charged conductors. The photos show
patterns for
a. equal and opposite charges;
b. equal like charges;
c. oppositely charged plates;
33.2 Electric Field Lines
33 Electric Fields and Potential
You can demonstrate electric field patterns
by suspending fine thread in an oil bath with
charged conductors. The photos show
patterns for
a. equal and opposite charges;
b. equal like charges;
c. oppositely charged plates;
d. oppositely charged cylinder and plate.
33.2 Electric Field Lines
33 Electric Fields and Potential
Bits of thread suspended in an oil bath surrounding charged
conductors line up end-to-end with the field lines.
Oppositely charged parallel plates produce nearly parallel field
lines between the plates. Except near the ends, the field
between the plates has a constant strength.
There is no electric field inside a charged cylinder. The
conductor shields the space from the field outside.
33.2 Electric Field Lines
33 Electric Fields and Potential
think! A beam of electrons is produced at one end of a glass tube and lights up a
phosphor screen at the other end. If the beam passes through the electric
field of a pair of oppositely charged plates, it is deflected upward as shown.
If the charges on the plates are reversed, in what direction will the beam
deflect?
33.2 Electric Field Lines
33 Electric Fields and Potential
think! A beam of electrons is produced at one end of a glass tube and lights up a
phosphor screen at the other end. If the beam passes through the electric
field of a pair of oppositely charged plates, it is deflected upward as shown.
If the charges on the plates are reversed, in what direction will the beam
deflect?
Answer:
When the charge on the plates is reversed, the electric field will be in the
opposite direction, so the electron beam will be deflected upward.
33.2 Electric Field Lines
33 Electric Fields and Potential
How can you represent an electric field?
33.2 Electric Field Lines
33 Electric Fields and Potential
If the charge on a conductor is not moving, the
electric field inside the conductor is exactly zero.
33.3 Electric Shielding
33 Electric Fields and Potential
When a car is struck by
lightning, the occupant inside
the car is completely safe.
The electrons that shower
down upon the car are
mutually repelled and spread
over the outer metal surface.
It discharges when additional
sparks jump to the ground.
The electric fields inside the
car practically cancel to zero.
33.3 Electric Shielding
33 Electric Fields and Potential
Charged Conductors
The absence of electric field within a conductor holding static
charge is not an inability of an electric field to penetrate
metals.
Free electrons within the conductor can “settle down” and stop
moving only when the electric field is zero.
The charges arrange to ensure a zero field with the material.
33.3 Electric Shielding
33 Electric Fields and Potential
Consider a charged metal sphere.
Because of repulsion, electrons
spread as far apart as possible,
uniformly over the surface.
A positive test charge located exactly
in the middle of the sphere would feel
no force. The net force on a test
charge would be zero.
The electric field is also zero.
Complete cancellation will occur
anywhere inside the sphere.
33.3 Electric Shielding
33 Electric Fields and Potential
If the conductor is not spherical, the charge distribution will not
be uniform but the electric field inside the conductor is zero.
If there were an electric field inside a conductor, then free
electrons inside the conductor would be set in motion.
They would move to establish equilibrium, that is, all the
electrons produce a zero field inside the conductor.
33.3 Electric Shielding
33 Electric Fields and Potential
How to Shield an Electric Field
There is no way to shield gravity, because gravity
only attracts.
Shielding electric fields, however, is quite simple.
• Surround yourself or whatever you wish to
shield with a conducting surface.
• Put this surface in an electric field of whatever
field strength.
• The free charges in the conducting surface will
arrange on the surface of the conductor so that
fields inside cancel.
33.3 Electric Shielding
33 Electric Fields and Potential
The metal-lined cover
shields the internal
electrical components
from external electric
fields. A metal cover
shields the cable.
33.3 Electric Shielding
33 Electric Fields and Potential
think!
It is said that a gravitational field, unlike an electric field,
cannot be shielded. But the gravitational field at the center of
Earth cancels to zero. Isn’t this evidence that a gravitational
field can be shielded?
33.3 Electric Shielding
33 Electric Fields and Potential
think!
It is said that a gravitational field, unlike an electric field,
cannot be shielded. But the gravitational field at the center of
Earth cancels to zero. Isn’t this evidence that a gravitational
field can be shielded?
Answer:
No. Gravity can be canceled inside a planet or between
planets, but it cannot be shielded. Shielding requires a
combination of repelling and attracting forces, and gravity
only attracts.
33.3 Electric Shielding
33 Electric Fields and Potential
How can you describe the electric field within a
conductor holding static charge?
33.3 Electric Shielding
33 Electric Fields and Potential
The electrical potential energy of a charged particle
is increased when work is done to push it against
the electric field of something else that is charged.
33.4 Electrical Potential Energy
33 Electric Fields and Potential
Work is done when a force moves something in the
direction of the force.
An object has potential energy by virtue of its location,
say in a force field.
For example, doing work by lifting an object increases
its gravitational potential energy.
33.4 Electrical Potential Energy
33 Electric Fields and Potential
a. In an elevated position, the ram has gravitational
potential energy. When released, this energy is
transferred to the pile below.
33.4 Electrical Potential Energy
33 Electric Fields and Potential
a. In an elevated position, the ram has gravitational
potential energy. When released, this energy is
transferred to the pile below.
b. Similar energy transfer occurs for electric charges.
33.4 Electrical Potential Energy
33 Electric Fields and Potential
A charged object can have potential energy by virtue of
its location in an electric field.
Work is required to push a charged particle against the
electric field of a charged body.
33.4 Electrical Potential Energy
33 Electric Fields and Potential
To push a positive test charge closer to a
positively charged sphere, we will expend
energy to overcome electrical repulsion.
Work is done in pushing the charge against
the electric field.
This work is equal to the energy gained by
the charge.
The energy a charge has due to its location
in an electric field is called
electrical potential energy.
If the charge is released, it will accelerate
away from the sphere and electrical potential
energy transforms into kinetic energy.
33.4 Electrical Potential Energy
33 Electric Fields and Potential
How can you increase the electrical potential
energy of a charged particle?
33.4 Electrical Potential Energy
33 Electric Fields and Potential
Electric potential is not the same as electrical
potential energy. Electric potential is electrical
potential energy per charge.
33.5 Electric Potential
33 Electric Fields and Potential
If we push a single charge against an electric field, we
do a certain amount of work. If we push two charges
against the same field, we do twice as much work.
Two charges in the same location in an electric field will
have twice the electrical potential energy as one; ten
charges will have ten times the potential energy.
It is convenient when working with electricity to consider
the electrical potential energy per charge.
33.5 Electric Potential
33 Electric Fields and Potential
The electrical potential energy per charge is the total electrical
potential energy divided by the amount of charge.
At any location the potential energy per charge—whatever the
amount of charge—will be the same.
The concept of electrical potential energy per charge has the
name, electric potential.
33.5 Electric Potential
33 Electric Fields and Potential
An object of greater charge has more electrical potential
energy in the field of the charged dome than an object of less
charge, but the electric potential of any charge at the same
location is the same.
33.5 Electric Potential
33 Electric Fields and Potential
The SI unit of measurement for electric potential is the
volt, named after the Italian physicist Allesandro Volta.
The symbol for volt is V.
Potential energy is measured in joules and charge is
measured in coulombs,
33.5 Electric Potential
33 Electric Fields and Potential
A potential of 1 volt equals 1 joule of energy per coulomb of charge.
A potential of 1000 V means that 1000 joules of energy per coulomb is
needed to bring a small charge from very far away and add it to the charge
on the conductor.
The small charge would be much less than one coulomb, so the energy
required would be much less than 1000 joules.
To add one proton to the conductor would take only 1.6 × 10–16 J.
33.5 Electric Potential
33 Electric Fields and Potential
Since electric potential is measured in volts, it is
commonly called voltage.
Once the location of zero voltage has been specified, a
definite value for it can be assigned to a location
whether or not a charge exists at that location.
We can speak about the voltages at different locations
in an electric field whether or not any charges occupy
those locations.
33.5 Electric Potential
33 Electric Fields and Potential
Rub a balloon on your hair and the
balloon becomes negatively charged,
perhaps to several thousand volts!
The charge on a balloon rubbed on
hair is typically much less than a
millionth of a coulomb.
Therefore, the energy is very small—
about a thousandth of a joule.
A high voltage requires great energy
only if a great amount of charge is
involved.
33.5 Electric Potential
33 Electric Fields and Potential
think! If there were twice as much charge on one of the
objects, would the electrical potential energy be
the same or would it be twice as great? Would
the electric potential be the same or would it be
twice as great?
33.5 Electric Potential
33 Electric Fields and Potential
think! If there were twice as much charge on one of the
objects, would the electrical potential energy be
the same or would it be twice as great? Would
the electric potential be the same or would it be
twice as great?
Answer:
Twice as much charge would cause the object to
have twice as much electrical potential energy,
because it would have taken twice as much work
to bring the object to that location. The electric
potential would be the same, because the electric
potential is total electrical potential energy divided
by total charge.
33.5 Electric Potential
33 Electric Fields and Potential
What is the difference between electric potential
and electrical potential energy?
33.5 Electric Potential
33 Electric Fields and Potential
The energy stored in a capacitor comes from the
work done to charge it.
33.6 Electrical Energy Storage
33 Electric Fields and Potential
Electrical energy can be stored in a device called a capacitor.
• Computer memories use very tiny capacitors to store the
1’s and 0’s of the binary code.
• Capacitors in photoflash units store larger amounts of
energy slowly and release it rapidly during the flash.
• Enormous amounts of energy are stored in banks of
capacitors that power giant lasers in national
laboratories.
33.6 Electrical Energy Storage
33 Electric Fields and Potential
The simplest capacitor is a pair of
conducting plates separated by a small
distance, but not touching each other.
• Charge is transferred from one plate
to the other.
• The capacitor plates then have
equal and opposite charges.
• The charging process is complete
when the potential difference
between the plates equals the
potential difference between the
battery terminals—the battery
voltage.
• The greater the battery voltage and
the larger and closer the plates, the
greater the charge that is stored.
33.6 Electrical Energy Storage
33 Electric Fields and Potential
In practice, the plates may be thin metallic foils separated by a
thin sheet of paper.
This “paper sandwich” is then rolled up to save space and may
be inserted into a cylinder.
33.6 Electrical Energy Storage
33 Electric Fields and Potential
A charged capacitor is discharged when a conducing path is
provided between the plates.
Discharging a capacitor can be a shocking experience if you
happen to be the conducting path.
The energy transfer can be fatal where voltages are high, such
as the power supply in a TV set—even if the set has been
turned off.
33.6 Electrical Energy Storage
33 Electric Fields and Potential
The energy stored in a capacitor comes from the
work done to charge it.
The energy is in the form of the electric field
between its plates.
Electric fields are storehouses of energy.
33.6 Electrical Energy Storage
33 Electric Fields and Potential
Where does the energy stored in a capacitor
come from?
33.6 Electrical Energy Storage
33 Electric Fields and Potential
The voltage of a Van de Graaff generator can be
increased by increasing the radius of the sphere or
by placing the entire system in a container filled
with high-pressure gas.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
A common laboratory device for building up high voltages is
the Van de Graaff generator.
This is the lightning machine often used by “evil scientists” in
old science fiction movies.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
In a Van de Graaff generator, a moving rubber belt carries
electrons from the voltage source to a conducting sphere.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
A large hollow metal sphere is supported by a cylindrical
insulating stand.
A rubber belt inside the support stand moves past metal
needles that are maintained at a high electric potential.
A continuous supply of electrons is deposited on the belt
through electric discharge by the points of the needles.
The electrons are carried up into the hollow metal sphere.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
The electrons leak onto metal points attached to the inner
surface of the sphere.
Because of mutual repulsion, the electrons move to the outer
surface of the conducting sphere.
This leaves the inside surface uncharged and able to receive
more electrons.
The process is continuous, and the charge builds up to a very
high electric potential—on the order of millions of volts.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
The physics enthusiast and the dome of the Van de Graaff
generator are charged to a high voltage.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
A sphere with a radius of 1 m can be raised to a potential of 3
million volts before electric discharge occurs through the air.
The voltage of a Van de Graaff generator can be increased by
increasing the radius of the sphere or by placing the entire
system in a container filled with highpressure gas.
Van de Graaff generators in pressurized gas can produce
voltages as high as 20 million volts. These devices accelerate
charged particles used as projectiles for penetrating the nuclei
of atoms.
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
How can the voltage of a Van de Graaff generator
be increased?
33.7 The Van de Graaff Generator
33 Electric Fields and Potential
1. An electric field has
a. no direction.
b. only magnitude.
c. both magnitude and direction.
d. a uniformed strength throughout.
Assessment Questions
33 Electric Fields and Potential
1. An electric field has
a. no direction.
b. only magnitude.
c. both magnitude and direction.
d. a uniformed strength throughout.
Answer: C
Assessment Questions
33 Electric Fields and Potential
2. In the electric field surrounding a group of charged particles, field
strength is greater where field lines are
a. thickest.
b. longest.
c. farthest apart.
d. closest.
Assessment Questions
33 Electric Fields and Potential
2. In the electric field surrounding a group of charged particles, field
strength is greater where field lines are
a. thickest.
b. longest.
c. farthest apart.
d. closest.
Answer: D
Assessment Questions
33 Electric Fields and Potential
3. Electrons on the surface of a conductor will arrange themselves such
that the electric field
a. inside cancels to zero.
b. follows the inverse-square law.
c. tends toward a state of minimum energy.
d. is shielded from external charges.
Assessment Questions
33 Electric Fields and Potential
3. Electrons on the surface of a conductor will arrange themselves such
that the electric field
a. inside cancels to zero.
b. follows the inverse-square law.
c. tends toward a state of minimum energy.
d. is shielded from external charges.
Answer: A
Assessment Questions
33 Electric Fields and Potential
4. The potential energy of a compressed spring and the potential
energy of a charged object both depend
a. only on the work done on them.
b. only on their locations in their respective fields.
c. on their locations in their respective fields and on the work
done on them.
d. on their kinetic energies exceeding their potential energies.
Assessment Questions
33 Electric Fields and Potential
4. The potential energy of a compressed spring and the potential
energy of a charged object both depend
a. only on the work done on them.
b. only on their locations in their respective fields.
c. on their locations in their respective fields and on the work
done on them.
d. on their kinetic energies exceeding their potential energies.
Answer: C
Assessment Questions
33 Electric Fields and Potential
5. Electric potential is related to electrical potential energy as
a. the two terms are different names for the same concept.
b. electric potential is the ratio of electrical potential energy per
charge.
c. both are measured using the units of coulomb.
d. both are measured using only the units of joules.
Assessment Questions
33 Electric Fields and Potential
5. Electric potential is related to electrical potential energy as
a. the two terms are different names for the same concept.
b. electric potential is the ratio of electrical potential energy per
charge.
c. both are measured using the units of coulomb.
d. both are measured using only the units of joules.
Answer: B
Assessment Questions
33 Electric Fields and Potential
6. A capacitor
a. cannot store charge.
b. cannot store energy.
c. can only store energy.
d. can store energy and charge.
Assessment Questions
33 Electric Fields and Potential
6. A capacitor
a. cannot store charge.
b. cannot store energy.
c. can only store energy.
d. can store energy and charge.
Answer: D
Assessment Questions
33 Electric Fields and Potential
7. What happens to the electric field inside the conducting sphere of a
Van de Graaff generator as it charges?
a. The field increases in magnitude as the amount of
charge increases.
b. The field decreases in magnitude as the amount of
charge increases.
c. The field will have a net force of one.
d. Nothing; the field is always zero.
Assessment Questions
33 Electric Fields and Potential
7. What happens to the electric field inside the conducting sphere of a
Van de Graaff generator as it charges?
a. The field increases in magnitude as the amount of
charge increases.
b. The field decreases in magnitude as the amount of
charge increases.
c. The field will have a net force of one.
d. Nothing; the field is always zero.
Answer: D
Assessment Questions
34 Electric Current
Electric current is related to
the voltage that produces it,
and the resistance that
opposes it.
34 Electric Current
Voltage produces a flow of charge, or current, within a conductor. The flow is restrained by the resistance it encounters. The rate at which energy is transferred by electric current is power.
34 Electric Current
When the ends of an electric conductor are at
different electric potentials, charge flows from one
end to the other.
34.1 Flow of Charge
34 Electric Current
Heat flows through a conductor when a temperature
difference exists. Heat flows from higher temperature to lower
temperature.
When temperature is at equilibrium, the flow of heat ceases.
34.1 Flow of Charge
34 Electric Current
Charge flows in a similar way. Charge flows
when there is a potential difference, or
difference in potential (voltage), between the
ends of a conductor. The flow continues until
both ends reach the same potential.
When there is no potential difference, there is
no longer a flow of charge through the
conductor.
To attain a sustained flow of charge in a
conductor, one end must remain at a higher
potential than the other.
The situation is analogous to the flow of water.
34.1 Flow of Charge
34 Electric Current
a. Water flows from higher pressure to lower pressure. The
flow will cease when the difference in pressure ceases.
34.1 Flow of Charge
34 Electric Current
a. Water flows from higher pressure to lower pressure. The
flow will cease when the difference in pressure ceases.
b. Water continues to flow because a difference in pressure
is maintained with the pump. The same is true of electric
current.
34.1 Flow of Charge
34 Electric Current
What happens when the ends of a conductor are
at different electrical potentials?
34.1 Flow of Charge
34 Electric Current
A current-carrying wire has a
net electric charge of zero.
34.2 Electric Current
34 Electric Current
Electric current is the flow of electric charge.
In solid conductors, electrons carry the charge through the
circuit because they are free to move throughout the atomic
network.
These electrons are called conduction electrons.
Protons are bound inside atomic nuclei, locked in fixed
positions.
In fluids, such as the electrolyte in a car battery, positive and
negative ions as well as electrons may flow.
34.2 Electric Current
34 Electric Current
Measuring Current
Electric current is measured in
amperes, symbol A.
An ampere is the flow of
1 coulomb of charge per second.
When the flow of charge past any
cross section is 1 coulomb (6.24
billion billion electrons) per
second, the current is 1 ampere.
34.2 Electric Current
34 Electric Current
Net Charge of a Wire
While the current is flowing, negative electrons swarm
through the atomic network of positively charged
atomic nuclei.
Under ordinary conditions, the number of electrons in
the wire is equal to the number of positive protons in
the atomic nuclei.
As electrons flow, the number entering is the same as
the number leaving, so the net charge is normally zero
at every moment.
34.2 Electric Current
34 Electric Current
What is the net flow of electric charge in a
current-carrying wire?
34.2 Electric Current
34 Electric Current
Voltage sources such as batteries and generators
supply energy that allows charges to move steadily.
34.3 Voltage Sources
34 Electric Current
Charges do not flow unless there is a potential difference.
Something that provides a potential difference is known as a
voltage source.
Batteries and generators are capable of maintaining a
continuous flow of electrons.
34.3 Voltage Sources
34 Electric Current
Steady Voltage Sources
In a battery, a chemical reaction releases electrical energy.
Generators—such as the alternators in automobiles—convert
mechanical energy to electrical energy.
The electrical potential energy produced is available at the
terminals of the battery or generator.
34.3 Voltage Sources
34 Electric Current
The potential energy per
coulomb of charge available to
electrons moving between
terminals is the voltage.
The voltage provides the
“electric pressure” to move
electrons between the terminals
in a circuit.
34.3 Voltage Sources
34 Electric Current
Power utilities use electric generators to provide the 120 volts
delivered to home outlets.
The alternating potential difference between the two holes in
the outlet averages 120 volts.
When the prongs of a plug are inserted into the outlet, an
average electric “pressure” of 120 volts is placed across the
circuit.
This means that 120 joules of energy is supplied to each
coulomb of charge that is made to flow in the circuit.
34.3 Voltage Sources
34 Electric Current
Distinguishing Between Current and Voltage
There is often some confusion between charge flowing
through a circuit and voltage being impressed across a circuit.
34.3 Voltage Sources
34 Electric Current
Consider a long pipe filled with water.
• Water will flow through the pipe if there is a difference in
pressure across the pipe or between its ends.
• Water flows from high pressure to low pressure.
Similarly, charges flow through a circuit because of an applied
voltage across the circuit.
• You don’t say that voltage flows through a circuit.
• Voltage doesn’t go anywhere, for it is the charges that
move.
• Voltage causes current.
34.3 Voltage Sources
34 Electric Current
What are two voltage sources used to provide
the energy that allows charges to move steadily?
34.3 Voltage Sources
34 Electric Current
The resistance of a wire depends on the
conductivity of the material used in the wire (that
is, how well it conducts) and also on the thickness
and length of the wire.
34.4 Electric Resistance
34 Electric Current
The amount of charge that flows in a circuit depends on the
voltage provided by the voltage source.
The current also depends on the resistance that the conductor
offers to the flow of charge—the electric resistance.
This is similar to the rate of water flow in a pipe, which
depends on the pressure difference and on the resistance of
the pipe.
34.4 Electric Resistance
34 Electric Current
For a given pressure, more
water passes through a
large pipe than a small
one. Similarly, for a given
voltage, more electric
current passes through a
large-diameter wire than a
small-diameter one.
34.4 Electric Resistance
34 Electric Current
A simple hydraulic circuit is analogous to an electric circuit.
34.4 Electric Resistance
34 Electric Current
The resistance of a wire depends on the conductivity of the
material in the wire and on the thickness and length of the
wire.
• Thick wires have less resistance than thin wires.
• Longer wires have more resistance than short wires.
• Electric resistance also depends on temperature. For
most conductors, increased temperature means
increased resistance.
34.4 Electric Resistance
34 Electric Current
The resistance of some materials becomes zero at very
low temperatures, a phenomenon known as
superconductivity.
Certain metals acquire superconductivity (zero
resistance to the flow of charge) at temperatures near
absolute zero.
Superconductivity at “high” temperatures (above 100 K)
has been found in a variety of nonmetallic compounds.
In a superconductor, the electrons flow indefinitely.
34.4 Electric Resistance
34 Electric Current
What factors affect the resistance of a wire?
34.4 Electric Resistance
34 Electric Current
Ohm’s law states that the current in a circuit is
directly proportional to the voltage impressed
across the circuit, and is inversely proportional to
the resistance of the circuit.
34.5 Ohm’s Law
34 Electric Current
Electric resistance is measured in units called ohms.
Georg Simon Ohm, a German physicist, tested wires in circuits
to see what effect the resistance of the wire had on the current.
The relationship among voltage, current, and resistance is
called Ohm’s law.
34.5 Ohm’s Law
34 Electric Current
For a given circuit of constant resistance, current and
voltage are proportional.
Twice the current flows through a circuit for twice the
voltage across the circuit. The greater the voltage, the
greater the current.
If the resistance is doubled for a circuit, the current will
be half what it would be otherwise.
34.5 Ohm’s Law
34 Electric Current
The relationship among the units of measurement is:
A potential difference of 1 volt impressed across a circuit that
has a resistance of 1 ohm will produce a current of 1 ampere.
If a voltage of 12 volts is impressed across the same circuit,
the current will be 12 amperes.
34.5 Ohm’s Law
34 Electric Current
The resistance of a typical lamp cord is much less than 1 ohm,
while a typical light bulb has a resistance of about 100 ohms.
An iron or electric toaster has a resistance of 15 to 20 ohms.
The low resistance permits a large current, which produces
considerable heat.
34.5 Ohm’s Law
34 Electric Current
Current inside electric devices is regulated by circuit elements
called resistors.
The stripes on these resistors are color coded to indicate the
resistance in ohms.
34.5 Ohm’s Law
34 Electric Current
think!
How much current is drawn by a lamp that has a resistance of
100 ohms when a voltage of 50 volts is impressed across it?
34.5 Ohm’s Law
34 Electric Current
think!
How much current is drawn by a lamp that has a resistance of
100 ohms when a voltage of 50 volts is impressed across it?
Answer:
34.5 Ohm’s Law
34 Electric Current
What does Ohm’s law state?
34.5 Ohm’s Law
34 Electric Current
The damaging effects of electric shock are the
result of current passing through the body.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
From Ohm’s law, we
can see that current
depends on the voltage
applied, and also on the
electric resistance of
the human body.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
The Body’s Resistance
Your body’s resistance ranges from about 100 ohms if soaked with salt
water to about 500,000 ohms if your skin is very dry.
Touch the electrodes of a battery with dry fingers and your resistance to
the flow of charge would be about 100,000 ohms.
You would not feel 12 volts, and 24 volts would just barely tingle.
With moist skin, however, 24 volts could be quite uncomfortable.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Many people are killed each year by current from common
120-volt electric circuits.
Touch a faulty 120-volt light fixture while standing on the
ground and there is a 120-volt “pressure” between you and
the ground.
The soles of your shoes normally provide a very large
resistance, so the current would probably not be enough to do
serious harm.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
If you are standing barefoot in a wet bathtub, the resistance
between you and the ground is very small.
Your overall resistance is so low that the 120-volt potential
difference may produce a harmful current through your body.
Drops of water that collect around the on/off switches of
devices such as a hair dryer can conduct current to the user.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Although distilled water is a good insulator, the ions in
ordinary water greatly reduce the electric resistance.
There is also usually a layer of salt on your skin, which
when wet lowers your skin resistance to a few hundred
ohms or less.
Handling electric devices while taking a bath is
extremely dangerous.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Handling a wet hair dryer can be like sticking your
fingers into a live socket.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
High-Voltage Wires
You probably have seen birds
perched on high-voltage wires.
Every part of the bird’s body is at the
same high potential as the wire, and
it feels no ill effects.
For the bird to receive a shock, there
must be a difference in potential
between one part of its body and
another part.
Most of the current will then pass
along the path of least electric
resistance connecting these two
points.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Suppose you fall from a bridge and manage to grab onto
a high-voltage power line, halting your fall.
If you touch nothing else of different potential, you will
receive no shock, even if the wire is thousands of volts
above ground potential.
No charge will flow from one hand to the other because
there is no appreciable difference in electric potential
between your hands.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Ground Wires
Mild shocks occur when the surfaces of appliances are at an
electric potential different from other nearby devices.
If you touch surfaces of different potentials, you become a
pathway for current.
To prevent this, electric appliances are connected to a
ground wire, through the round third prong of a three-wire
electric plug.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
All ground wires in all plugs are connected together through
the wiring system of the house.
The two flat prongs are for the current-carrying double wire.
If the live wire accidentally comes in contact with the metal
surface of an appliance, the current will be directed to ground
rather than shocking you if you handle it.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Health Effects
One effect of electric shock is to overheat tissues in the body
or to disrupt normal nerve functions.
It can upset the nerve center that controls breathing.
34.6 Ohm’s Law and Electric Shock
34 Electric Current
think!
If the resistance of your body were 100,000 ohms, what would
be the current in your body when you touched the terminals of
a 12-volt battery?
34.6 Ohm’s Law and Electric Shock
34 Electric Current
think!
If the resistance of your body were 100,000 ohms, what would
be the current in your body when you touched the terminals of
a 12-volt battery?
Answer:
34.6 Ohm’s Law and Electric Shock
34 Electric Current
think!
If your skin were very moist, so that your resistance was only
1000 ohms, and you touched the terminals of a 24-volt battery,
how much current would you draw?
34.6 Ohm’s Law and Electric Shock
34 Electric Current
think!
If your skin were very moist, so that your resistance was only
1000 ohms, and you touched the terminals of a 24-volt battery,
how much current would you draw?
Answer:
You would draw
or 0.024 A, a dangerous amount of current!
34.6 Ohm’s Law and Electric Shock
34 Electric Current
What causes the damaging effects
of electric shock?
34.6 Ohm’s Law and Electric Shock
34 Electric Current
Electric current may be DC or AC.
34.7 Direct Current and Alternating Current
34 Electric Current
By DC, we mean direct current, which refers to a flow of charge that
always flows in one direction.
• A battery produces direct current in a circuit because the terminals
of the battery always have the same sign of charge.
• Electrons always move through the circuit from the negative
terminal toward the positive terminal.
• Even if the current moves in unsteady pulses, so long as it moves
in one direction only, it is DC.
34.7 Direct Current and Alternating Current
34 Electric Current
Alternating current (AC), as the name implies, is electric current that
repeatedly reverses direction.
• Electrons in the circuit move first in one direction and then in the
opposite direction.
• They alternate back and forth about relatively fixed positions.
• This is accomplished by alternating the polarity of voltage at the
generator or other voltage source.
34.7 Direct Current and Alternating Current
34 Electric Current
Voltage Standards
Voltage of AC in North America is normally 120 volts.
In the early days of electricity, higher voltages burned out the
filaments of electric light bulbs.
Power plants in the United States prior to 1900 adopted 110
volts (or 115 or 120 volts) as standard.
34.7 Direct Current and Alternating Current
34 Electric Current
By the time electricity became popular in Europe, light
bulbs were available that would not burn out so fast at
higher voltages.
Power transmission is more efficient at higher voltages,
so Europe adopted 220 volts as their standard.
The United States stayed with 110 volts (today, officially
120 volts) because of the installed base of 110-volt
equipment.
34.7 Direct Current and Alternating Current
34 Electric Current
Three-Wire Service
Although lamps in an American home operate on 110–120
volts, electric stoves and other appliances operate on 220–
240 volts.
Most electric service in the United States is three-wire:
• one wire at 120 volts positive
• one wire at zero volts (neutral)
• one wire at a negative 120 volts
34.7 Direct Current and Alternating Current
34 Electric Current
In AC, the positive and negative alternate at 60 hertz. A
wire that is positive at one instant is negative 1/120 of a
second later.
Most home appliances are connected between the
neutral wire and either of the other two wires, producing
120 volts.
When the plus-120 is connected to the minus-120, it
produces a 240-volt difference—just right for electric
stoves, air conditioners, and clothes dryers.
34.7 Direct Current and Alternating Current
34 Electric Current
The popularity of AC arises from the fact that electrical energy
in the form of AC can be transmitted great distances.
Easy voltage step-ups result in lower heat losses in the wires.
The primary use of electric current, whether DC or AC, is to
transfer energy from one place to another.
34.7 Direct Current and Alternating Current
34 Electric Current
What are the two types of electric current?
34.7 Direct Current and Alternating Current
34 Electric Current
With an AC-DC converter, you can operate a
battery-run device on AC instead of batteries.
34.8 Converting AC to DC
34 Electric Current
The current in your home is AC. The current in a battery-
operated device, such as a laptop computer or cell phone,
is DC.
With an AC-DC converter, you can operate a battery-run
device on AC instead of batteries.
34.8 Converting AC to DC
34 Electric Current
A converter uses a transformer to
lower the voltage and a diode, an
electronic device that allows
electron flow in only one direction.
Since alternating current vibrates in
two directions, only half of each
cycle will pass through a diode.
The output is a rough DC, off half
the time.
To maintain continuous current
while smoothing the bumps, a
capacitor is used.
34.8 Converting AC to DC
34 Electric Current
Recall that a capacitor acts as a storage reservoir for charge.
Just as it takes time to raise or lower the water level in a
reservoir, it takes time to add or remove electrons from the
capacitor.
A capacitor therefore produces a retarding effect on changes
in current flow and smoothes the pulsed output.
34.8 Converting AC to DC
34 Electric Current
a. When input to a diode is AC,
34.8 Converting AC to DC
34 Electric Current
a. When input to a diode is AC,
b. output is pulsating DC.
34.8 Converting AC to DC
34 Electric Current
a. When input to a diode is AC,
b. output is pulsating DC.
c. Charging and discharging of a capacitor provides
continuous and smoother current.
34.8 Converting AC to DC
34 Electric Current
a. When input to a diode is AC,
b. output is pulsating DC.
c. Charging and discharging of a capacitor provides
continuous and smoother current.
d. In practice, a pair of diodes is used so there are no gaps
in current output.
34.8 Converting AC to DC
34 Electric Current
How can you operate a battery-run
device on AC?
34.8 Converting AC to DC
34 Electric Current
In a current-carrying wire, collisions interrupt the
motion of the electrons so that their actual drift
speed, or net speed through the wire due to the
field, is extremely low.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
When you flip on the light switch on your wall and the circuit is
completed, the light bulb appears to glow immediately.
Energy is transported through the connecting wires at nearly
the speed of light.
The electrons that make up the current, however, do not move
at this high speed.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
The electrons inside a metal wire have an average speed of a
few million kilometers per hour due to their thermal motion.
This does not produce a current because the motion is
random. There is no net flow in any one direction.
When a battery or generator is connected, an electric field is
established inside the wire.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
A pulsating electric field can travel through a circuit at nearly
the speed of light.
The electrons continue their random motions in all directions
while simultaneously being nudged along the wire by the
electric field.
The conducting wire acts as a “pipe” for electric field lines.
Inside the wire, the electric field is directed along the wire.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
The electric field lines between the terminals of a battery are
directed through a conductor, which joins the terminals.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
Conduction electrons are accelerated by the field.
Before the electrons gain appreciable speed, they “bump into”
metallic ions and transfer some of their kinetic energy.
• Collisions interrupt the motion of the electrons. Their
actual drift speed, or net speed through the wire, is
extremely low.
• In the electric system of an automobile, electrons have a
net average drift speed of about 0.01 cm/s.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
The solid lines depict a random path of an electron bouncing
off atoms in a conductor. The dashed lines show an
exaggerated view of how this path changes when an electric
field is applied. The electron drifts toward the right with an
average speed less than a snail’s pace.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
In an AC circuit, the conduction electrons don’t
make any net progress in any direction.
• In a single cycle they drift a tiny fraction of a
centimeter in one direction, and then the same
distance in the opposite direction.
• They oscillate rhythmically about relatively
fixed positions.
• On a conventional telephone, it is the pattern
of oscillating motion that is carried at nearly
the speed of light.
• The electrons in the wires vibrate to the
rhythm of the traveling pattern.
34.9 The Speed of Electrons in a Circuit
34 Electric Current
Why is the drift speed of electrons in a
current-carrying wire extremely low?
34.9 The Speed of Electrons in a Circuit
34 Electric Current
The source of electrons in a circuit is the
conducting circuit material itself.
34.10 The Source of Electrons in a Circuit
34 Electric Current
You can buy a water hose that is empty of water, but
you can’t buy a piece of wire, an “electron pipe,” that is
empty of electrons.
The source of electrons in a circuit is the conducting
circuit material itself.
Electrons do not travel appreciable distances through a
wire in an AC circuit. They vibrate to and fro about
relatively fixed positions.
34.10 The Source of Electrons in a Circuit
34 Electric Current
When you plug a lamp into an AC outlet,
energy flows from the outlet into the lamp,
not electrons.
Energy is carried by the electric field and
causes a vibratory motion of the electrons
that already exist in the lamp filament.
Most of this electrical energy appears as
heat, while some of it takes the form of
light.
Power utilities do not sell electrons. They
sell energy. You supply the electrons.
34.10 The Source of Electrons in a Circuit
34 Electric Current
When you are jolted by an AC electric shock, the
electrons making up the current in your body originate
in your body.
Electrons do not come out of the wire and through your
body and into the ground; energy does.
The energy simply causes free electrons in your body to
vibrate in unison.
Small vibrations tingle; large vibrations can be fatal.
34.10 The Source of Electrons in a Circuit
34 Electric Current
What is the source of electrons in a circuit?
34.10 The Source of Electrons in a Circuit
34 Electric Current
Electric power is equal to the product of
current and voltage.
34.11 Electric Power
34 Electric Current
Unless it is in a superconductor, a charge moving in a circuit
expends energy.
This may result in heating the circuit or in turning a motor.
Electric power is the rate at which electrical energy is
converted into another form such as mechanical energy,
heat, or light.
34.11 Electric Power
34 Electric Current
Electric power is equal to the product of current and voltage.
electric power = current × voltage
If the voltage is expressed in volts and the current in
amperes, then the power is expressed in watts.
1 watt = (1 ampere) × (1 volt)
34.11 Electric Power
34 Electric Current
The power and voltage on the light bulb read “60 W 120 V.”
The current that would flow through the bulb is:
I = P/V = (60 W)/(120 V) = 0.5 A.
34.11 Electric Power
34 Electric Current
A lamp rated at 120 watts operated
on a 120-volt line will draw a current
of 1 ampere:
120 watts = (1 ampere) × (120 volts).
A 60-watt lamp draws 0.5 ampere on
a 120-volt line.
34.11 Electric Power
34 Electric Current
A kilowatt is 1000 watts, and a kilowatt-hour represents the
amount of energy consumed in 1 hour at the rate
of 1 kilowatt.
Where electrical energy costs 10 cents per kilowatt-hour, a
100-watt light bulb burns for 10 hours for 10 cents.
A toaster or iron, which draws more current and therefore
more power, costs several times as much to operate for the
same time.
34.11 Electric Power
34 Electric Current
think!
How much power is used by a calculator that operates on 8
volts and 0.1 ampere? If it is used for one hour, how much
energy does it use?
34.11 Electric Power
34 Electric Current
think!
How much power is used by a calculator that operates on 8
volts and 0.1 ampere? If it is used for one hour, how much
energy does it use?
Answer:
Power = current × voltage = (0.1 A) × (8 V) = 0.8 W.
Energy = power × time = (0.8 W) × (1 h) = 0.8 watt-hour,
or 0.0008 kilowatt-hour.
34.11 Electric Power
34 Electric Current
think!
Will a 1200-watt hair dryer operate on a 120-volt line if the
current is limited to 15 amperes by a safety fuse? Can two hair
dryers operate on this line?
34.11 Electric Power
34 Electric Current
think!
Will a 1200-watt hair dryer operate on a 120-volt line if the
current is limited to 15 amperes by a safety fuse? Can two hair
dryers operate on this line?
Answer:
One 1200-W hair dryer can be operated because the circuit
can provide (15 A) × (120 V) = 1800 W. But there is
inadequate power to operate two hair dryers of combined
power 2400 W. In terms of current, (1200 W)/(120 V) = 10 A;
so the hair dryer will operate when connected to the circuit. But
two hair dryers will require 20 A and will blow the 15-A fuse.
34.11 Electric Power
34 Electric Current
How can you express electric power in terms of
current and voltage?
34.11 Electric Power
34 Electric Current
1. Electric charge will flow in an electric circuit when
a. electrical resistance is low enough.
b. a potential difference exists.
c. the circuit is grounded.
d. electrical devices in the circuit are not defective.
Assessment Questions
34 Electric Current
1. Electric charge will flow in an electric circuit when
a. electrical resistance is low enough.
b. a potential difference exists.
c. the circuit is grounded.
d. electrical devices in the circuit are not defective.
Answer: B
Assessment Questions
34 Electric Current
2. The electric current in a copper wire is normally composed of
a. electrons.
b. protons.
c. ions.
d. amperes.
Assessment Questions
34 Electric Current
2. The electric current in a copper wire is normally composed of
a. electrons.
b. protons.
c. ions.
d. amperes.
Answer: A
Assessment Questions
34 Electric Current
3. Which statement is correct?
a. Voltage flows in a circuit.
b. Charge flows in a circuit.
c. A battery is the source of electrons in a circuit.
d. A generator is the source of electrons in a circuit.
Assessment Questions
34 Electric Current
3. Which statement is correct?
a. Voltage flows in a circuit.
b. Charge flows in a circuit.
c. A battery is the source of electrons in a circuit.
d. A generator is the source of electrons in a circuit.
Answer: B
Assessment Questions
34 Electric Current
4. Which of the following type of copper wire would you expect to
have the least electric resistance?
a. a thick long wire
b. a thick short wire
c. a thin long wire
d. a thin short wire
Assessment Questions
34 Electric Current
4. Which of the following type of copper wire would you expect to
have the least electric resistance?
a. a thick long wire
b. a thick short wire
c. a thin long wire
d. a thin short wire
Answer: D
Assessment Questions
34 Electric Current
5. When you double the voltage in a simple electric circuit, you
double the
a. current.
b. resistance.
c. ohms.
d. resistors.
Assessment Questions
34 Electric Current
5. When you double the voltage in a simple electric circuit, you
double the
a. current.
b. resistance.
c. ohms.
d. resistors.
Answer: A
Assessment Questions
34 Electric Current
6. To receive an electric shock there must be
a. current in one direction.
b. moisture in an electrical device being used.
c. high voltage and low body resistance.
d. a difference in potential across part or all of your body.
Assessment Questions
34 Electric Current
6. To receive an electric shock there must be
a. current in one direction.
b. moisture in an electrical device being used.
c. high voltage and low body resistance.
d. a difference in potential across part or all of your body.
Answer: D
Assessment Questions
34 Electric Current
7. The difference between DC and AC in electrical circuits is that
in DC
a. charges flow steadily in one direction only.
b. charges flow in one direction.
c. charges steadily flow to and fro.
d. charges flow to and fro.
Assessment Questions
34 Electric Current
7. The difference between DC and AC in electrical circuits is that
in DC
a. charges flow steadily in one direction only.
b. charges flow in one direction.
c. charges steadily flow to and fro.
d. charges flow to and fro.
Answer: B
Assessment Questions
34 Electric Current
8. To convert AC to a fairly steady DC, which devices are used?
a. diodes and batteries
b. capacitors and diodes
c. capacitors and batteries
d. resistors and batteries
Assessment Questions
34 Electric Current
8. To convert AC to a fairly steady DC, which devices are used?
a. diodes and batteries
b. capacitors and diodes
c. capacitors and batteries
d. resistors and batteries
Answer: B
Assessment Questions
34 Electric Current
9. What is it that travels at about the speed of light in an electric circuit?
a. charges
b. current
c. electric field
d. voltage
Assessment Questions
34 Electric Current
9. What is it that travels at about the speed of light in an electric circuit?
a. charges
b. current
c. electric field
d. voltage
Answer: C
Assessment Questions
34 Electric Current
10. When you buy a water pipe in a hardware store, the water
isn’t included. When you buy copper wire, electrons
a. must be supplied by you, just as water must be supplied
for a water pipe.
b. are already in the wire.
c. may fall out, which is why wires are insulated.
d. enter it from the electric outlet.
Assessment Questions
34 Electric Current
10. When you buy a water pipe in a hardware store, the water
isn’t included. When you buy copper wire, electrons
a. must be supplied by you, just as water must be supplied
for a water pipe.
b. are already in the wire.
c. may fall out, which is why wires are insulated.
d. enter it from the electric outlet.
Answer: B
Assessment Questions
34 Electric Current
11. If you double both the current and the voltage in a circuit, the power
a. remains unchanged if resistance remains constant.
b. halves.
c. doubles.
d. quadruples.
Assessment Questions
34 Electric Current
11. If you double both the current and the voltage in a circuit, the power
a. remains unchanged if resistance remains constant.
b. halves.
c. doubles.
d. quadruples.
Answer: D
Assessment Questions
35 Electric Circuits
Any path along
which electrons can
flow is a circuit.
35 Electric Circuits
Mechanical things seem to be easier to figure out for most people than electrical things. Maybe this is because most people have had experience playing with blocks and mechanical toys. Hands-on laboratory experience aids your understanding of electric circuits. The experience can be a lot of fun, too!
35 Electric Circuits
In a flashlight, when the switch is turned on to
complete an electric circuit, the mobile conduction
electrons already in the wires and the filament begin
to drift through the circuit.
35.1 A Battery and a Bulb
35 Electric Circuits
A flashlight consists of a reflector cap, a light bulb, batteries,
and a barrel-shaped housing with a switch.
35.1 A Battery and a Bulb
35 Electric Circuits
There are several ways to connect the battery and bulb from
a flashlight so that the bulb lights up.
The important thing is that there must be a complete path, or
circuit, that
• includes the bulb filament
• runs from the positive terminal at the top of the battery
• runs to the negative terminal at the bottom of the battery
35.1 A Battery and a Bulb
35 Electric Circuits
Electrons flow
• from the negative part of the battery through the wire
• to the side (or bottom) of the bulb
• through the filament inside the bulb
• out the bottom (or side)
• through the wire to the positive part of the battery
The current then passes through the battery to complete
the circuit.
35.1 A Battery and a Bulb
35 Electric Circuits
a. Unsuccessful ways to light a bulb.
35.1 A Battery and a Bulb
35 Electric Circuits
a. Unsuccessful ways to light a bulb.
b. Successful ways to light a bulb.
35.1 A Battery and a Bulb
35 Electric Circuits
The flow of charge in a circuit is very much like the flow of
water in a closed system of pipes.
In a flashlight, the battery is analogous to a pump, the wires
are analogous to the pipes, and the bulb is analogous to
any device that operates when the water is flowing.
When a valve in the line is opened and the pump is
operating, water already in the pipes starts to flow.
35.1 A Battery and a Bulb
35 Electric Circuits
Neither the water nor the electrons
concentrate in certain places.
They flow continuously around a
loop, or circuit.
When the switch is turned on, the
mobile conduction electrons in the
wires and the filament begin to drift
through the circuit.
35.1 A Battery and a Bulb
35 Electric Circuits
Electrons do not pile up inside
a bulb, but instead flow through
its filament.
35.1 A Battery and a Bulb
35 Electric Circuits
What happens to the mobile conduction
electrons when you turn on a flashlight?
35.1 A Battery and a Bulb
35 Electric Circuits
For a continuous flow of electrons, there must
be a complete circuit with no gaps.
35.2 Electric Circuits
35 Electric Circuits
Any path along which electrons can
flow is a circuit.
A gap is usually provided by an
electric switch that can be opened
or closed to either cut off or allow
electron flow.
35.2 Electric Circuits
35 Electric Circuits
The water analogy is useful but has some limitations.
• A break in a water pipe results in a leak, but a
break in an electric circuit results in a complete
stop in the flow.
• Opening a switch stops the flow of electricity. An
electric circuit must be closed for electricity to
flow. Opening a water faucet, on the other hand,
starts the flow of water.
35.2 Electric Circuits
35 Electric Circuits
Most circuits have more than one device that receives
electrical energy.
These devices are commonly connected in a circuit in
one of two ways, series or parallel.
• When connected in series, the devices in a
circuit form a single pathway for electron flow.
• When connected in parallel, the devices in a
circuit form branches, each of which is a
separate path for electron flow.
35.2 Electric Circuits
35 Electric Circuits
How can a circuit achieve a continuous
flow of electrons?
35.2 Electric Circuits
35 Electric Circuits
If one device fails in a series circuit, current in
the whole circuit ceases and none of the
devices will work.
35.3 Series Circuits
35 Electric Circuits
If three lamps are connected in series with a battery,
they form a series circuit. Charge flows through each
in turn.
When the switch is closed, a current exists almost
immediately in all three lamps.
The current does not “pile up” in any lamp but flows
through each lamp. Electrons in all parts of the circuit
begin to move at once.
35.3 Series Circuits
35 Electric Circuits
Eventually the electrons move all the way around the circuit.
A break anywhere in the path results in an open circuit, and
the flow of electrons ceases.
Burning out of one of the lamp filaments or simply opening
the switch could cause such a break.
35.3 Series Circuits
35 Electric Circuits
In this simple series circuit, a 9-volt battery provides 3 volts
across each lamp.
35.3 Series Circuits
35 Electric Circuits
For series connections:
• Electric current has a single pathway through the circuit.
• The total resistance to current in the circuit is the sum of
the individual resistances along the circuit path.
• The current is equal to the voltage supplied by the source
divided by the total resistance of the circuit. This is Ohm’s
law.
• The voltage drop, or potential difference, across each
device depends directly on its resistance.
• The sum of the voltage drops across the individual
devices is equal to the total voltage supplied by the
source.
35.3 Series Circuits
35 Electric Circuits
The main disadvantage of a
series circuit is that when one
device fails, the current in the
whole circuit stops.
Some cheap light strings are
connected in series. When one
lamp burns out, you have to
replace it or no lights work.
35.3 Series Circuits
35 Electric Circuits
think!
What happens to the light intensity of each lamp in a series
circuit when more lamps are added to the circuit?
35.3 Series Circuits
35 Electric Circuits
think!
What happens to the light intensity of each lamp in a series
circuit when more lamps are added to the circuit?
Answer:
The addition of more lamps results in a greater circuit
resistance. This decreases the current in the circuit (and in
each lamp), which causes dimming of the lamps.
35.3 Series Circuits
35 Electric Circuits
think!
A series circuit has three bulbs. If the current through one of
the bulbs is 1 A, can you tell what the current is through each
of the other two bulbs? If the voltage across bulb 1 is 2 V, and
across bulb 2 is 4 V, what is the voltage across bulb 3?
35.3 Series Circuits
35 Electric Circuits
think!
A series circuit has three bulbs. If the current through one of
the bulbs is 1 A, can you tell what the current is through each
of the other two bulbs? If the voltage across bulb 1 is 2 V, and
across bulb 2 is 4 V, what is the voltage across bulb 3?
Answer:
The same current, 1 A, passes through every part of a series
circuit. Each coulomb of charge has 9 J of electrical potential
energy (9 V = 9 J/C). If it spends 2 J in one bulb and 4 in
another, it must spend 3 J in the last bulb. 3 J/C = 3 V
35.3 Series Circuits
35 Electric Circuits
What happens to current in other lamps if
one lamp in a series circuit burns out?
35.3 Series Circuits
35 Electric Circuits
In a parallel circuit, each device operates
independent of the other devices. A break in any
one path does not interrupt the flow of charge in
the other paths.
35.4 Parallel Circuits
35 Electric Circuits
In a parallel circuit having three lamps, each electric
device has its own path from one terminal of the battery
to the other.
There are separate pathways for current, one through
each lamp.
In contrast to a series circuit, the parallel circuit is
completed whether all, two, or only one lamp is lit.
A break in any one path does not interrupt the flow of
charge in the other paths.
35.4 Parallel Circuits
35 Electric Circuits
In this parallel circuit, a 9-volt battery provides 9 volts
across each activated lamp. (Note the open switch in the
lower branch.)
35.4 Parallel Circuits
35 Electric Circuits
Major characteristics of parallel connections:
• Each device connects the same two points A and B of
the circuit. The voltage is therefore the same across
each device.
• The total current divides among the parallel branches.
• The amount of current in each branch is inversely
proportional to the resistance of the branch.
• The total current is the sum of the currents in its
branches.
• As the number of parallel branches is increased, the
total current through the battery increases.
35.4 Parallel Circuits
35 Electric Circuits
From the battery’s perspective, the overall resistance of the
circuit is decreased.
This means the overall resistance of the circuit is less than the
resistance of any one of the branches.
35.4 Parallel Circuits
35 Electric Circuits
think!
What happens to the light intensity of each lamp in a parallel
circuit when more lamps are added in parallel to the circuit?
35.4 Parallel Circuits
35 Electric Circuits
think!
What happens to the light intensity of each lamp in a parallel
circuit when more lamps are added in parallel to the circuit?
Answer:
The light intensity for each lamp is unchanged as other lamps
are introduced (or removed). Although changes of resistance
and current occur for the circuit as a whole, no changes occur
in any individual branch in the circuit.
35.4 Parallel Circuits
35 Electric Circuits
What happens if one device in a parallel
circuit fails?
35.4 Parallel Circuits
35 Electric Circuits
In a schematic diagram, resistance is shown by a
zigzag line, and ideal resistance-free wires are shown
with solid straight lines. A battery is represented with
a set of short and long parallel lines.
35.5 Schematic Diagrams
35 Electric Circuits
Electric circuits are frequently
described by simple diagrams, called
schematic diagrams.
• Resistance is shown by a
zigzag line, and ideal
resistance-free wires are shown
with solid straight lines.
• A battery is shown by a set of
short and long parallel lines, the
positive terminal with a long line
and the negative terminal with a
short line.
35.5 Schematic Diagrams
35 Electric Circuits
These schematic diagrams represent
a. a circuit with three lamps in series, and
35.5 Schematic Diagrams
35 Electric Circuits
These schematic diagrams represent
a. a circuit with three lamps in series, and
b. a circuit with three lamps in parallel.
35.5 Schematic Diagrams
35 Electric Circuits
What symbols are used to represent resistance,
wires, and batteries in schematic diagrams?
35.5 Schematic Diagrams
35 Electric Circuits
The equivalent resistance of resistors connected in
series is the sum of their values. The equivalent
resistance for a pair of equal resistors in parallel is
half the value of either resistor.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
Sometimes it is useful to know the equivalent resistance
of a circuit that has several resistors in its network.
The equivalent resistance is the value of the single
resistor that would comprise the same load to the battery
or power source.
The equivalent resistance of resistors connected in
series is the sum of their values. For example, the
equivalent resistance for a pair of 1-ohm resistors in
series is simply 2 ohms.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
The equivalent resistance for a pair of equal resistors in
parallel is half the value of either resistor.
The equivalent resistance for a pair of 1-ohm resistors in
parallel is 0.5 ohm.
The equivalent resistance is less because the current
has “twice the path width” when it takes the parallel path.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
a. The equivalent resistance of two 8-ohm resistors in
series is 16 ohms.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
a. The equivalent resistance of two 8-ohm resistors in
series is 16 ohms.
b. The equivalent resistance of two 8-ohm resistors in
parallel is 4 ohms.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
For the combination of three 8-ohm resistors, the two
resistors in parallel are equivalent to a single 4-ohm resistor.
They are in series with an 8-ohm resistor, adding to produce
an equivalent resistance of 12 ohms.
If a 12-volt battery were connected to these resistors, the
current through the battery would be 1 ampere.
(In practice it would be less, for there is resistance inside the
battery as well, called the battery’s internal resistance.)
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
Schematic diagrams for an arrangement of various electric
devices. The equivalent resistance of the circuit is 10 ohms.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
think!
In the circuit shown below, what is the current in amperes
through the pair of 10-ohm resistors? Through each of the 8-
ohm resistors?
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
think!
In the circuit shown below, what is the current in amperes
through the pair of 10-ohm resistors? Through each of the 8-
ohm resistors?
Answer:
The total resistance of the middle branch is 20 Ω. Since the
voltage is 60 V, the current = (voltage)/(resistance) =
(60V)/(2 Ω) = 3 A. The current through the pair of 8-Ω resistors
is 3 A, and the current through each is therefore 1.5 A.
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
What is the equivalent resistance of resistors in
series? Of equal resistors in parallel?
35.6 Combining Resistors in a Compound Circuit
35 Electric Circuits
To prevent overloading in circuits, fuses or
circuit breakers are connected in series along
the supply line.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
Electric current is fed into a home by two wires called lines.
About 110 to 120 volts are impressed on these lines at the
power utility.
These lines are very low in resistance and are connected to
wall outlets in each room.
The voltage is applied to appliances and other devices that
are connected in parallel by plugs to these lines.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
As more devices are connected to the lines, more
pathways are provided for current.
The additional pathways lower the combined resistance
of the circuit. Therefore, a greater amount of current
occurs in the lines.
Lines that carry more than a safe amount of current are
said to be overloaded, and may heat sufficiently to melt
the insulation and start a fire.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
Consider a line connected to a toaster that draws 8 amps, a heater that
draws 10 amps, and a lamp that draws 2 amps.
• If the toaster is operating, the total line current is 8 amperes.
• When the heater is also operating, the total line current increases to
18 amperes.
• If you turn on the lamp, the line current increases to 20 amperes.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
To prevent overloading in circuits, fuses or circuit breakers are
connected in series along the supply line.
The entire line current must pass through the fuse.
If the fuse is rated at 20 amperes, it will pass up to 20 amperes.
A current above 20 amperes will melt the fuse ribbon, which
“blows out” and breaks the circuit.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
Before a blown fuse is replaced, the cause of
overloading should be determined and remedied.
Insulation that separates the wires in a circuit can wear
away and allow the wires to touch.
This effectively shortens the path of the circuit, and is
called a short circuit.
A short circuit draws a dangerously large current
because it bypasses the normal circuit resistance.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
Circuits may also be protected by circuit breakers, which use
magnets or bimetallic strips to open the switch.
Utility companies use circuit breakers to protect their lines all
the way back to the generators.
Circuit breakers are used in modern buildings because they
do not have to be replaced each time the circuit is opened.
35.7 Parallel Circuits and Overloading
35 Electric Circuits
How can you prevent overloading in circuits?
35.7 Parallel Circuits and Overloading
35 Electric Circuits
1. In a light bulb, the amount of current in the filament is
a. slightly less than the current in the connecting wires.
b. the same as the current in the connecting wires.
c. slightly greater than the current in the connecting wires.
d. twice as great as the current that is in the connecting wires.
Assessment Questions
35 Electric Circuits
1. In a light bulb, the amount of current in the filament is
a. slightly less than the current in the connecting wires.
b. the same as the current in the connecting wires.
c. slightly greater than the current in the connecting wires.
d. twice as great as the current that is in the connecting wires.
Answer: B
Assessment Questions
35 Electric Circuits
2. The flow of charge in an electric circuit is
a. much like the flow of water in a system of pipes.
b. very different from water flow in pipes.
c. like an electric valve.
d. like an electric pump.
Assessment Questions
35 Electric Circuits
2. The flow of charge in an electric circuit is
a. much like the flow of water in a system of pipes.
b. very different from water flow in pipes.
c. like an electric valve.
d. like an electric pump.
Answer: A
Assessment Questions
35 Electric Circuits
3. In a series circuit, if the current in one lamp is 2 amperes, the current
in the battery is
a. half, 1 A.
b. 2 A.
c. not necessarily 2 A, depending on internal battery resistance.
d. more than 2 A.
Assessment Questions
35 Electric Circuits
3. In a series circuit, if the current in one lamp is 2 amperes, the current
in the battery is
a. half, 1 A.
b. 2 A.
c. not necessarily 2 A, depending on internal battery resistance.
d. more than 2 A.
Answer: B
Assessment Questions
35 Electric Circuits
4. In a circuit with two lamps in parallel, if the current in one lamp is
2 amperes, the current in the battery is
a. half, 1 A.
b. 2 A.
c. more than 2 A.
d. cannot be calculated from the information given
Assessment Questions
35 Electric Circuits
4. In a circuit with two lamps in parallel, if the current in one lamp is
2 amperes, the current in the battery is
a. half, 1 A.
b. 2 A.
c. more than 2 A.
d. cannot be calculated from the information given
Answer: C
Assessment Questions
35 Electric Circuits
5. In a circuit diagram there may be
a. no switches.
b. at most, one switch.
c. two switches.
d. any number of switches.
Assessment Questions
35 Electric Circuits
5. In a circuit diagram there may be
a. no switches.
b. at most, one switch.
c. two switches.
d. any number of switches.
Answer: D
Assessment Questions
35 Electric Circuits
6. Consider a compound circuit consisting of a pair of 6-ohm resistors in
parallel, which are in series with two 6-ohm resistors in series. The
equivalent resistance of the circuit is
a. 9 ohms.
b. 12 ohms.
c. 15 ohms.
d. 24 ohms.
Assessment Questions
35 Electric Circuits
6. Consider a compound circuit consisting of a pair of 6-ohm resistors in
parallel, which are in series with two 6-ohm resistors in series. The
equivalent resistance of the circuit is
a. 9 ohms.
b. 12 ohms.
c. 15 ohms.
d. 24 ohms.
Answer: C
Assessment Questions
35 Electric Circuits
7. One way to prevent overloading in your home circuit is to
a. operate fewer devices at the same time.
b. change the wiring from parallel to series for troublesome
devices.
c. find a way to bypass the fuse.
d. find a way to bypass the circuit breaker.
Assessment Questions
35 Electric Circuits
7. One way to prevent overloading in your home circuit is to
a. operate fewer devices at the same time.
b. change the wiring from parallel to series for troublesome
devices.
c. find a way to bypass the fuse.
d. find a way to bypass the circuit breaker.
Answer: A
Assessment Questions
36 Magnetism
A moving electric charge
is surrounded by a
magnetic field.
36 Magnetism
Electricity and magnetism were regarded as unrelated phenomena until it was noticed that an electric current caused the deflection of the compass needle. Then, magnets were found to exert forces on current-carrying wires. The stage was set for a whole new technology, which would eventually bring electric power, radio, and television.
36 Magnetism
Like poles repel; opposite poles attract.
36.1 Magnetic Poles
36 Magnetism
Magnets exert forces on one another.
They are similar to electric charges, for they can both attract
and repel without touching.
Like electric charges, the strength of their interaction depends
on the distance of separation of the two magnets.
Electric charges produce electrical forces and regions called
magnetic poles produce magnetic forces.
36.1 Magnetic Poles
36 Magnetism
Which interaction has the greater strength—the gravitational
attraction between the scrap iron and Earth, or the magnetic
attraction between the magnet and the scrap iron?
36.1 Magnetic Poles
36 Magnetism
If you suspend a bar magnet from its center by a
piece of string, it will act as a compass.
• The end that points northward is called the
north-seeking pole.
• The end that points southward is called the
south-seeking pole.
• More simply, these are called the north and
south poles.
• All magnets have both a north and a south
pole. For a simple bar magnet the poles are
located at the two ends.
36.1 Magnetic Poles
36 Magnetism
If the north pole of one magnet is brought near the north pole of another
magnet, they repel.
The same is true of a south pole near a south pole.
If opposite poles are brought together, however, attraction occurs.
36.1 Magnetic Poles
36 Magnetism
Magnetic poles behave similarly to electric charges in some
ways, but there is a very important difference.
• Electric charges can be isolated, but magnetic poles
cannot.
• A north magnetic pole never exists without the presence
of a south pole, and vice versa.
• The north and south poles of a magnet are like the head
and tail of the same coin.
36.1 Magnetic Poles
36 Magnetism
If you break a bar magnet in half, each half still behaves as a
complete magnet.
Break the pieces in half again, and you have four complete
magnets.
Even when your piece is one atom thick, there are two poles.
This suggests that atoms themselves are magnets.
36.1 Magnetic Poles
36 Magnetism
36.1 Magnetic Poles
36 Magnetism
think!
Does every magnet necessarily have a north
and a south pole?
36.1 Magnetic Poles
36 Magnetism
think!
Does every magnet necessarily have a north
and a south pole?
Answer:
Yes, just as every coin has two sides, a “head”
and a “tail.” (Some “trick” magnets have more
than two poles.)
36.1 Magnetic Poles
36 Magnetism
How do magnetic poles affect each other?
36.1 Magnetic Poles
36 Magnetism
The direction of the magnetic field outside a
magnet is from the north to the south pole.
36.2 Magnetic Fields
36 Magnetism
Iron filings sprinkled on a sheet of paper over a bar magnet will
tend to trace out a pattern of lines that surround the magnet.
The space around a magnet, in which a magnetic force is
exerted, is filled with a magnetic field.
The shape of the field is revealed by magnetic field lines.
36.2 Magnetic Fields
36 Magnetism
Magnetic field lines spread out from one pole, curve around
the magnet, and return to the other pole.
36.2 Magnetic Fields
36 Magnetism
Magnetic field patterns for a pair of magnets when
a. opposite poles are near each other
36.2 Magnetic Fields
36 Magnetism
Magnetic field patterns for a pair of magnets when
a. opposite poles are near each other
b. like poles are near each other
36.2 Magnetic Fields
36 Magnetism
The direction of the magnetic field
outside a magnet is from the north
to the south pole.
Where the lines are closer together,
the field strength is greater.
The magnetic field strength is
greater at the poles.
If we place another magnet or a
small compass anywhere in the
field, its poles will tend to line up
with the magnetic field.
36.2 Magnetic Fields
36 Magnetism
What is the direction of the magnetic field
outside a magnet?
36.2 Magnetic Fields
36 Magnetism
A magnetic field is produced by the motion of
electric charge.
36.3 The Nature of a Magnetic Field
36 Magnetism
Magnetism is very much related to electricity.
Just as an electric charge is surrounded by an electric
field, a moving electric charge is also surrounded by a
magnetic field.
Charges in motion have associated with them both an
electric and a magnetic field.
36.3 The Nature of a Magnetic Field
36 Magnetism
Electrons in Motion
Where is the motion of electric charges in a common
bar magnet?
The magnet as a whole may be stationary, but it is
composed of atoms whose electrons are in constant
motion about atomic nuclei.
This moving charge constitutes a tiny current and
produces a magnetic field.
36.3 The Nature of a Magnetic Field
36 Magnetism
More important, electrons can be thought of as spinning
about their own axes like tops.
A spinning electron creates another magnetic field.
In most materials, the field due to spinning
predominates over the field due to orbital motion.
36.3 The Nature of a Magnetic Field
36 Magnetism
Spin Magnetism
Every spinning electron is a tiny magnet.
• A pair of electrons spinning in the same direction
makes up a stronger magnet.
• Electrons spinning in opposite directions work
against one another.
• Their magnetic fields cancel.
36.3 The Nature of a Magnetic Field
36 Magnetism
Most substances are not magnets because the various
fields cancel one another due to electrons spinning in
opposite directions.
In materials such as iron, nickel, and cobalt, however,
the fields do not cancel one another entirely.
An iron atom has four electrons whose spin magnetism
is not canceled.
Each iron atom, then, is a tiny magnet. The same is true
to a lesser degree for the atoms of nickel and cobalt.
36.3 The Nature of a Magnetic Field
36 Magnetism
How is a magnetic field produced?
36.3 The Nature of a Magnetic Field
36 Magnetism
Permanent magnets are made by simply placing
pieces of iron or certain iron alloys in strong
magnetic fields.
36.4 Magnetic Domains
36 Magnetism
The magnetic fields of individual iron atoms are strong.
• Interactions among adjacent iron atoms cause
large clusters of them to line up with one another.
• These clusters of aligned atoms are called
magnetic domains.
• Each domain is perfectly magnetized, and is made
up of billions of aligned atoms.
• The domains are microscopic, and there are many
of them in a crystal of iron.
36.4 Magnetic Domains
36 Magnetism
The difference between a piece of ordinary iron and an iron magnet is the
alignment of domains.
• In a common iron nail, the domains are randomly oriented.
• When a strong magnet is brought nearby, there is a growth in size of
domains oriented in the direction of the magnetic field.
• The domains also become aligned much as electric dipoles are aligned in
the presence of a charged rod.
• When you remove the nail from the magnet, thermal motion causes most of
the domains to return to a random arrangement.
36.4 Magnetic Domains
36 Magnetism
Permanent magnets are made by simply placing pieces
of iron or certain iron alloys in strong magnetic fields.
Another way of making a permanent magnet is to stroke
a piece of iron with a magnet.
The stroking motion aligns the domains in the iron.
If a permanent magnet is dropped or heated, some of
the domains are jostled out of alignment and the
magnet becomes weaker.
36.4 Magnetic Domains
36 Magnetism
The arrows represent
domains, where the
head is a north pole
and the tail a south
pole. Poles of
neighboring domains
neutralize one
another’s effects,
except at the ends.
36.4 Magnetic Domains
36 Magnetism
think!
Iron filings sprinkled on paper that covers a magnet were not
initially magnetized. Why, then, do they line up with the
magnetic field of the magnet?
36.4 Magnetic Domains
36 Magnetism
think!
Iron filings sprinkled on paper that covers a magnet were not
initially magnetized. Why, then, do they line up with the
magnetic field of the magnet?
Answer:
Domains align in the individual filings, causing them to act like
tiny compasses. The poles of each “compass” are pulled in
opposite directions, producing a torque that twists each filing
into alignment with the external magnetic field.
36.4 Magnetic Domains
36 Magnetism
How can you make a permanent magnet?
36.4 Magnetic Domains
36 Magnetism
An electric current produces a magnetic field.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
A moving charge produces a magnetic field.
An electric current passing through a conductor
produces a magnetic field because it has many charges
in motion.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
The magnetic field surrounding a current-carrying
conductor can be shown by arranging magnetic
compasses around the wire.
The compasses line up with the magnetic field
produced by the current, a pattern of concentric circles
about the wire.
When the current reverses direction, the compasses
turn around, showing that the direction of the magnetic
field changes also.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
a. When there is no current in the wire, the compasses
align with Earth’s magnetic field.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
a. When there is no current in the wire, the compasses
align with Earth’s magnetic field.
b. When there is a current in the wire, the compasses
align with the stronger magnetic field near the wire.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
If the wire is bent into a loop, the magnetic field lines become bunched up
inside the loop.
If the wire is bent into another loop, the concentration of magnetic field lines
inside the double loop is twice that of the single loop.
The magnetic field intensity increases as the number of loops is increased.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
A current-carrying coil of wire is an electromagnet.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
Iron filings sprinkled on paper reveal the magnetic field
configurations about
a.a current-carrying wire
36.5 Electric Currents and Magnetic Fields
36 Magnetism
Iron filings sprinkled on paper reveal the magnetic field
configurations about
a.a current-carrying wire
b.a current-carrying loop
36.5 Electric Currents and Magnetic Fields
36 Magnetism
Iron filings sprinkled on paper reveal the magnetic field
configurations about
a.a current-carrying wire
b.a current-carrying loop
c. a coil of loops
36.5 Electric Currents and Magnetic Fields
36 Magnetism
Sometimes a piece of iron is placed inside the coil of
an electromagnet.
The magnetic domains in the iron are induced into
alignment, increasing the magnetic field intensity.
Beyond a certain limit, the magnetic field in iron
“saturates,” so iron is not used in the cores of the
strongest electromagnets.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
A superconducting electromagnet can generate a powerful
magnetic field indefinitely without using any power.
At Fermilab near Chicago, superconducting electromagnets
guide high-energy particles around the four-mile-
circumference accelerator.
Superconducting magnets can also be found in magnetic
resonance imaging (MRI) devices in hospitals.
36.5 Electric Currents and Magnetic Fields
36 Magnetism
Why does a current-carrying wire deflect a
magnetic compass?
36.5 Electric Currents and Magnetic Fields
36 Magnetism
A moving charge is deflected when it crosses
magnetic field lines but not when it travels
parallel to the field lines.
36.6 Magnetic Forces on Moving Charged Particles
36 Magnetism
If the charged particle moves in a magnetic field, the charged particle experiences
a deflecting force.
• This force is greatest when the particle moves in a direction perpendicular
to the magnetic field lines.
• At other angles, the force is less.
• The force becomes zero when the particle moves parallel to the field lines.
• The direction of the force is always perpendicular to both the magnetic
field lines and the velocity of the charged particle.
36.6 Magnetic Forces on Moving Charged Particles
36 Magnetism
The deflecting force is different from other forces,
such as the force of gravitation between masses, the
electrostatic force between charges, and the force
between magnetic poles.
The force that acts on a moving charged particle acts
perpendicular to both the magnetic field and the
electron velocity.
36.6 Magnetic Forces on Moving Charged Particles
36 Magnetism
The deflection of charged
particles by magnetic fields
provides a TV picture.
Charged particles from outer
space are deflected by Earth’s
magnetic field, which reduces the
intensity of cosmic radiation.
A much greater reduction in
intensity results from the
absorption of cosmic rays in the
atmosphere.
36.6 Magnetic Forces on Moving Charged Particles
36 Magnetism
What happens when a charged particle moves in
a magnetic field?
36.6 Magnetic Forces on Moving Charged Particles
36 Magnetism
Since a charged particle moving through a magnetic
field experiences a deflecting force, a current of
charged particles moving through a magnetic field
also experiences a deflecting force.
36.7 Magnetic Forces on Current-Carrying Wires
36 Magnetism
If the particles are inside a wire, the wire will also move.
• If the direction of current in the wire is reversed, the deflecting force acts in
the opposite direction.
• The force is maximum when the current is perpendicular to the magnetic
field lines.
• The direction of force is along neither the magnetic field lines nor the
direction of current.
• The force is perpendicular to both field lines and current, and it is a
sideways force.
36.7 Magnetic Forces on Current-Carrying Wires
36 Magnetism
Just as a current-carrying wire will deflect a magnetic
compass, a magnet will deflect a current-carrying wire.
Both cases show different effects of the same phenomenon.
The discovery that a magnet exerts a force on a current-
carrying wire created much excitement.
People began harnessing this force for useful purposes—
electric meters and electric motors.
36.7 Magnetic Forces on Current-Carrying Wires
36 Magnetism
think!
What law of physics tells you that if a current-carrying wire
produces a force on a magnet, a magnet must produce a force
on a current-carrying wire?
36.7 Magnetic Forces on Current-Carrying Wires
36 Magnetism
think!
What law of physics tells you that if a current-carrying wire
produces a force on a magnet, a magnet must produce a force
on a current-carrying wire?
Answer:
Newton’s third law, which applies to all forces in nature.
36.7 Magnetic Forces on Current-Carrying Wires
36 Magnetism
How is current affected by a magnetic field?
36.7 Magnetic Forces on Current-Carrying Wires
36 Magnetism
The principal difference between a galvanometer
and an electric motor is that in an electric motor, the
current is made to change direction every time the
coil makes a half revolution.
36.8 Meters to Motors
36 Magnetism
The simplest meter to detect electric current consists of a
magnetic needle on a pivot at the center of loops of
insulated wire.
When an electric current passes through the coil, each
loop produces its own effect on the needle.
A very small current can be detected. A sensitive current-
indicating instrument is called a galvanometer.
36.8 Meters to Motors
36 Magnetism
Common Galvanometers
A more common design employs more loops of wire
and is therefore more sensitive.
The coil is mounted for movement and the magnet is
held stationary.
The coil turns against a spring, so the greater the
current in its loops, the greater its deflection.
36.8 Meters to Motors
36 Magnetism
a. A common galvanometer consists of a stationary
magnet and a movable coil of wire.
36.8 Meters to Motors
36 Magnetism
a. A common galvanometer consists of a stationary
magnet and a movable coil of wire.
b. A multimeter can function as both an ammeter and a
voltmeter.
36.8 Meters to Motors
36 Magnetism
A galvanometer may be calibrated to measure current
(amperes), in which case it is called an ammeter.
Or it may be calibrated to measure electric potential (volts),
in which case it is called a voltmeter.
36.8 Meters to Motors
36 Magnetism
Electric Motors
If the design of the galvanometer is slightly modified, you have
an electric motor.
The principal difference is that in an electric motor, the current
changes direction every time the coil makes a half revolution.
After it has been forced to rotate one half revolution, it
overshoots just in time for the current to reverse.
The coil is forced to continue another half revolution, and so
on in cyclic fashion to produce continuous rotation.
36.8 Meters to Motors
36 Magnetism
In a simple DC motor, a permanent magnet produces a magnetic field in a
region where a rectangular loop of wire is mounted.
• The loop can turn about an axis.
• When a current passes through the loop, it flows in opposite
directions in the upper and lower sides of the loop.
• The loop is forced to move as if it were a galvanometer.
36.8 Meters to Motors
36 Magnetism
• The current is reversed during each half revolution by
means of stationary contacts on the shaft.
• The parts of the wire that brush against these contacts
are called brushes.
• The current in the loop alternates so that the forces in
the upper and lower regions do not change directions as
the loop rotates.
• The rotation is continuous as long as current is supplied.
36.8 Meters to Motors
36 Magnetism
Larger motors, DC or AC, are made by replacing the
permanent magnet with an electromagnet, energized by
the power source.
Many loops of wire are wound about an iron cylinder,
called an armature, which then rotates when energized
with electric current.
36.8 Meters to Motors
36 Magnetism
think!
How is a galvanometer similar to a simple electric motor? How
do they fundamentally differ?
36.8 Meters to Motors
36 Magnetism
think!
How is a galvanometer similar to a simple electric motor? How
do they fundamentally differ?
Answer:
A galvanometer and a motor are similar in that they both employ coils
positioned in magnetic fields. When current passes through the coils, forces
on the wires rotate the coils. The fundamental difference is that the
maximum rotation of the coil in a galvanometer is one half turn, whereas in
a motor the coil (armature) rotates through many complete turns. In the
armature of a motor, the current is made to change direction with each half
turn of the armature.
36.8 Meters to Motors
36 Magnetism
What is the main difference between a
galvanometer and an electric motor?
36.8 Meters to Motors
36 Magnetism
A compass points northward because Earth
itself is a huge magnet.
36.9 Earth’s Magnetic Field
36 Magnetism
The compass aligns with the magnetic
field of Earth, but the magnetic poles of
Earth do not coincide with the
geographic poles.
The magnetic pole in the Northern
Hemisphere, for example, is located
some 800 kilometers from the
geographic North Pole.
This means that compasses do not
generally point to true north.
The discrepancy is known as the
magnetic declination.
36.9 Earth’s Magnetic Field
36 Magnetism
Moving Changes Within Earth
The configuration of Earth’s magnetic field is like that of a
strong bar magnet placed near the center of Earth.
Earth is not a magnetized chunk of iron like a bar magnet. It is
simply too hot for individual atoms to remain aligned.
36.9 Earth’s Magnetic Field
36 Magnetism
Currents in the molten part of Earth beneath
the crust provide a better explanation for
Earth’s magnetic field.
Most geologists think that moving charges
looping around within Earth create its
magnetic field. Because of Earth’s great size,
the speed of charges would have to be less
than one millimeter per second to account for
the field.
Another possible cause for Earth’s magnetic
field is convection currents from the rising
heat of Earth’s core. Perhaps such
convection currents combined with the
rotational effects of Earth produce Earth’s
magnetic field.
36.9 Earth’s Magnetic Field
36 Magnetism
Magnetic Field Reversals
The magnetic field of Earth is not stable. Magnetic rock strata
show that it has flip-flopped throughout geologic time.
Iron atoms in a molten state align with Earth’s magnetic field.
When the iron solidifies, the direction of Earth’s field is
recorded by the orientation of the domains in the rock.
36.9 Earth’s Magnetic Field
36 Magnetism
On the ocean floor at mid-ocean ridges, continuous
eruption of lava produces new seafloor.
This new rock is magnetized by the existing magnetic field.
Alternating magnetic stripes show that there have been
times when the Earth’s magnetic field has dropped to zero
and then reversed.
36.9 Earth’s Magnetic Field
36 Magnetism
More than 20 reversals have taken place in the past 5 million
years. The most recent occurred 780,000 years ago.
We cannot predict when the next reversal will occur because
the reversal sequence is not regular.
Recent measurements show a decrease of over 5% of
Earth’s magnetic field strength in the last 100 years. If this
change is maintained, there may be another field reversal
within 2000 years.
36.9 Earth’s Magnetic Field
36 Magnetism
Why does a magnetic compass
point northward?
36.9 Earth’s Magnetic Field
36 Magnetism
1. For magnets, like poles repel each other and unlike poles
a. also repel each other.
b. attract each other.
c. can disappear into nothingness.
d. can carry a lot of energy.
Assessment Questions
36 Magnetism
1. For magnets, like poles repel each other and unlike poles
a. also repel each other.
b. attract each other.
c. can disappear into nothingness.
d. can carry a lot of energy.
Answer: B
Assessment Questions
36 Magnetism
2. The space surrounding a magnet is known as a(n)
a. electric field.
b. magnetic field.
c. magnetic pole.
d. electric pole.
Assessment Questions
36 Magnetism
2. The space surrounding a magnet is known as a(n)
a. electric field.
b. magnetic field.
c. magnetic pole.
d. electric pole.
Answer: B
Assessment Questions
36 Magnetism
3. Moving electric charges are surrounded by
a. only electric fields.
b. only magnetic fields.
c. both magnetic and electric fields.
d. nothing.
Assessment Questions
36 Magnetism
3. Moving electric charges are surrounded by
a. only electric fields.
b. only magnetic fields.
c. both magnetic and electric fields.
d. nothing.
Answer: C
Assessment Questions
36 Magnetism
4. The magnetic domains in a magnet produce a weaker magnet
when the
a. magnet is heated.
b. magnet is brought in contact with steel.
c. magnet is brought in contact with another strong magnet.
d. magnetic domains are all in alignment.
Assessment Questions
36 Magnetism
4. The magnetic domains in a magnet produce a weaker magnet
when the
a. magnet is heated.
b. magnet is brought in contact with steel.
c. magnet is brought in contact with another strong magnet.
d. magnetic domains are all in alignment.
Answer: A
Assessment Questions
36 Magnetism
5. The magnetic field lines about a current-carrying wire form
a. circles.
b. radial lines.
c. eddy currents.
d. spirals.
Assessment Questions
36 Magnetism
5. The magnetic field lines about a current-carrying wire form
a. circles.
b. radial lines.
c. eddy currents.
d. spirals.
Answer: A
Assessment Questions
36 Magnetism
6. A magnetic force cannot act on an electron when it moves
a. perpendicular to the magnetic field lines.
b. at an angle between 90° and 180° to the magnetic field lines.
c. at an angle between 45° and 90° to the magnetic field lines.
d. parallel to the magnetic field lines.
Assessment Questions
36 Magnetism
6. A magnetic force cannot act on an electron when it moves
a. perpendicular to the magnetic field lines.
b. at an angle between 90° and 180° to the magnetic field lines.
c. at an angle between 45° and 90° to the magnetic field lines.
d. parallel to the magnetic field lines.
Answer: D
Assessment Questions
36 Magnetism
7. A magnetic force acts most strongly on a current-carrying wire
when it is
a. parallel to the magnetic field.
b. perpendicular to the magnetic field.
c. at an angle to the magnetic field that is less than 90°.
d. at an angle to the magnetic field that is more than 90°.
Assessment Questions
36 Magnetism
7. A magnetic force acts most strongly on a current-carrying wire
when it is
a. parallel to the magnetic field.
b. perpendicular to the magnetic field.
c. at an angle to the magnetic field that is less than 90°.
d. at an angle to the magnetic field that is more than 90°.
Answer: B
Assessment Questions
36 Magnetism
8. Your teacher gives you two electrical machines and asks you to identify
which is a galvanometer and which is an electric motor. How can you tell the
difference between the two?
a. In a galvanometer, the current changes direction every time the
coil makes a half revolution.
b. In an electric motor, the current changes direction every time the
coil makes a half revolution.
c. In a galvanometer, the current changes direction every time the
coil makes a whole revolution.
d. In an electric motor, the current changes direction every time the coil
makes a whole revolution.
Assessment Questions
36 Magnetism
8. Your teacher gives you two electrical machines and asks you to identify
which is a galvanometer and which is an electric motor. How can you tell the
difference between the two?
a. In a galvanometer, the current changes direction every time the
coil makes a half revolution.
b. In an electric motor, the current changes direction every time the
coil makes a half revolution.
c. In a galvanometer, the current changes direction every time the
coil makes a whole revolution.
d. In an electric motor, the current changes direction every time the coil
makes a whole revolution.
Answer: B
Assessment Questions
36 Magnetism
9. The magnetic field surrounding Earth
a. is caused by magnetized chunks of iron in Earth’s crust.
b. is likely caused by magnetic declination.
c. never changes.
d. is likely caused by electric currents in its interior.
Assessment Questions
36 Magnetism
9. The magnetic field surrounding Earth
a. is caused by magnetized chunks of iron in Earth’s crust.
b. is likely caused by magnetic declination.
c. never changes.
d. is likely caused by electric currents in its interior.
Answer: D
Assessment Questions
37 Electromagnetic Induction
Magnetism can produce
electric current, and
electric current can
produce magnetism.
37 Electromagnetic Induction
In 1831, two physicists, Michael Faraday in England and Joseph Henry in the United States, independently discovered that magnetism could produce an electric current in a wire. Their discovery was to change the world by making electricity so commonplace that it would power industries by day and light up cities by night.
37 Electromagnetic Induction
Electric current can be produced in a wire by simply
moving a magnet into or out of a wire coil.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
No battery or other voltage
source was needed to produce a
current—only the motion of a
magnet in a coil or wire loop.
Voltage was induced by the
relative motion of a wire with
respect to a magnetic field.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
The production of voltage depends only on the relative motion
of the conductor with respect to the magnetic field.
Voltage is induced whether the magnetic field moves past a
conductor, or the conductor moves through a magnetic field.
The results are the same for the same relative motion.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
The amount of voltage induced depends on how quickly the
magnetic field lines are traversed by the wire.
• Very slow motion produces hardly any voltage at all.
• Quick motion induces a greater voltage.
Increasing the number of loops of wire that move in a
magnetic field increases the induced voltage and the current
in the wire.
Pushing a magnet into twice as many loops will induce twice
as much voltage.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
Twice as many loops as another means twice as much
voltage is induced. For a coil with three times as many loops,
three times as much voltage is induced.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
We don’t get something
(energy) for nothing by simply
increasing the number of loops
in a coil of wire.
Work is done because the
induced current in the loop
creates a magnetic field that
repels the approaching magnet.
If you try to push a magnet into
a coil with more loops, it
requires even more work.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
Work must be done to move the magnet.
a.Current induced in the loop produces a magnetic field
(the imaginary yellow bar magnet), which repels the bar magnet.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
Work must be done to move the magnet.
a.Current induced in the loop produces a magnetic field
(the imaginary yellow bar magnet), which repels the bar magnet.
b.When the bar magnet is pulled away, the induced
current is in the opposite direction and a magnetic field
attracts the bar magnet.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
The law of energy conservation applies here.
The force that you exert on the magnet multiplied by the
distance that you move the magnet is your input work.
This work is equal to the energy expended (or possibly
stored) in the circuit to which the coil is connected.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
If the coil is connected to a resistor, more induced voltage in
the coil means more current through the resistor.
That means more energy expenditure.
Inducing voltage by changing the magnetic field around a
conductor is electromagnetic induction.
37.1 Electromagnetic Induction
37 Electromagnetic Induction
How can you create a current using a
wire and a magnet?
37.1 Electromagnetic Induction
37 Electromagnetic Induction
Faraday’s law states that the induced voltage in
a coil is proportional to the product of the
number of loops, the cross-sectional area of
each loop, and the rate at which the magnetic
field changes within those loops.
37.2 Faraday’s Law
37 Electromagnetic Induction
Faraday’s law describes the relationship between
induced voltage and rate of change of a magnetic field:
The induced voltage in a coil is proportional to the product
of the number of loops, the cross-sectional area of each
loop, and the rate at which the magnetic field changes
within those loops.
37.2 Faraday’s Law
37 Electromagnetic Induction
The current produced by electromagnetic induction
depends upon
• the induced voltage,
• the resistance of the coil, and the circuit to
which it is connected.
For example, you can plunge a magnet in and out of
a closed rubber loop and in and out of a closed loop
of copper.
The voltage induced in each is the same but the
current is quite different—a lot in the copper but
almost none in the rubber.
37.2 Faraday’s Law
37 Electromagnetic Induction
think!
If you push a magnet into a coil connected to a resistor you’ll
feel a resistance to your push. For the same pushing speed,
why is this resistance greater in a coil with more loops?
37.2 Faraday’s Law
37 Electromagnetic Induction
think!
If you push a magnet into a coil connected to a resistor you’ll
feel a resistance to your push. For the same pushing speed,
why is this resistance greater in a coil with more loops?
Answer:
More work is required because more voltage is induced, producing more
current in the resistor and more energy transfer. When the magnetic fields
of two magnets overlap, the two magnets are either forced together or
forced apart. When one of the fields is induced by motion of the other, the
polarity of the fields is always such as to force the magnets apart. Inducing
more current in more coils increases the induced magnetic field and the
resistive force.
37.2 Faraday’s Law
37 Electromagnetic Induction
What does Faraday’s law state?
37.2 Faraday’s Law
37 Electromagnetic Induction
Whereas a motor converts electrical energy into
mechanical energy, a generator converts
mechanical energy into electrical energy.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
A current can be generated by plunging a magnet into and out
of a coil of wire.
• As the magnet enters, the magnetic field strength inside
the coil increases and induced voltage in the coil is
directed one way.
• As the magnet leaves, the magnetic field strength
diminishes and voltage is induced in the
opposite direction.
• Greater frequency of field change induces
greater voltage.
• The frequency of the alternating voltage is the frequency
of the changing magnetic field within the loop.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
It is more practical to move the coil instead of moving the
magnet, by rotating the coil in a stationary magnetic field.
A machine that produces electric current by rotating a coil
within a stationary magnetic field is called a generator.
A generator is essentially the opposite of a motor, converting
mechanical energy into electrical energy.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
Simple Generators
Starting perpendicular to the field, the loop has the largest
number of lines inside.
As it rotates, the loop encircles fewer of the field lines until it
lies along the field lines, when it encloses none at all.
As rotation continues, it encloses more field lines, reaching a
maximum when it has made a half revolution.
The magnetic field inside the loop changes in cyclic fashion.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
37.3 Generators and Alternating Current
37 Electromagnetic Induction
37.3 Generators and Alternating Current
37 Electromagnetic Induction
37.3 Generators and Alternating Current
37 Electromagnetic Induction
37.3 Generators and Alternating Current
37 Electromagnetic Induction
37.3 Generators and Alternating Current
37 Electromagnetic Induction
37.3 Generators and Alternating Current
37 Electromagnetic Induction
As the loop rotates, the magnitude and direction of the induced
voltage (and current) change. One complete rotation of the
loop produces one complete cycle in voltage (and current).
37.3 Generators and Alternating Current
37 Electromagnetic Induction
The voltage induced by the
generator alternates, and the current
produced is alternating current (AC).
The current changes magnitude and
direction periodically.
The standard AC in North America
changes magnitude and direction
during 60 complete cycles per
second—60 hertz.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
Complex Generators
The generators used in power plants are much more
complex than the model discussed here.
Huge coils made up of many loops of wire are wrapped on
an iron core, to make an armature much like the armature of
a motor.
They rotate in the very strong magnetic fields of powerful
electromagnets.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
The armature is connected externally to an assembly of paddle wheels
called a turbine.
While wind or falling water can be used to produce rotation of the turbine,
most commercial generators are driven by moving steam.
At the present time, a fossil fuel or nuclear fuel is used as the energy
source for the steam.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
An energy source of some kind is required to operate
a generator.
Some fraction of energy from the source is converted to
mechanical energy to drive the turbine.
The generator converts most of this to electrical energy.
Some people think that electricity is a source of energy. It is
not. It is a form of energy that must have a source.
37.3 Generators and Alternating Current
37 Electromagnetic Induction
How is a generator different from a motor?
37.3 Generators and Alternating Current
37 Electromagnetic Induction
Moving charges experience a force that is
perpendicular to both their motion and the
magnetic field they traverse.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
An electric current is deflected in a magnetic field,
which underlies the operation of the motor.
Electromagnetic induction underlies the operation of
a generator.
We will call the deflected wire the motor effect and
the law of induction the generator effect.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
a. When a current moves to the right, there is a force on the
electrons, and the wire is tugged upward.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
a. When a current moves to the right, there is a force on the
electrons, and the wire is tugged upward.
b. When a wire with no current is moved downward, the
electrons in the wire experience a force, creating current.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
The motor effect occurs when a current moves through a
magnetic field.
• The magnetic field creates a perpendicular upward
force on the electrons.
• Because the electrons can’t leave the wire, the
entire wire is tugged along with the electrons.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
In the generator effect, a wire with no current is moved
downward through a magnetic field.
• The electrons in this wire experience a force
perpendicular to their motion, which is along the wire.
• A current begins to flow.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
A striking example of a device functioning as both motor and
generator is found in hybrid automobiles.
• When extra power for accelerating or hill climbing is
needed, this device draws current from a battery and
acts as a motor.
• Braking or rolling downhill causes the wheels to exert a
torque on the device so it acts as a generator and
recharges the battery.
• The electrical part of the hybrid engine is both a motor
and a generator.
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
How does a magnetic field affect a
moving charge?
37.4 Motor and Generator Comparison
37 Electromagnetic Induction
A transformer works by inducing a changing
magnetic field in one coil, which induces an
alternating current in a nearby second coil.
37.5 Transformers
37 Electromagnetic Induction
Consider a pair of coils, side by side, one connected to a
battery and the other connected to a galvanometer.
It is customary to refer to the coil connected to the power
source as the primary (input), and the other as the
secondary (output).
37.5 Transformers
37 Electromagnetic Induction
As soon as the switch is closed in the primary and current
passes through its coil, a current occurs in the secondary.
When the primary switch is opened, a surge of current again
registers in the secondary but in the opposite direction.
Whenever the primary switch is opened or closed, voltage is
induced in the secondary circuit.
37.5 Transformers
37 Electromagnetic Induction
The magnetic field that builds up around the primary
extends into the secondary coil.
Changes in the magnetic field of the primary are sensed
by the nearby secondary.
These changes of magnetic field intensity at the
secondary induce voltage in the secondary, in accord
with Faraday’s law.
37.5 Transformers
37 Electromagnetic Induction
If we place an iron core inside
both coils, alignment of its
magnetic domains intensifies the
magnetic field within the primary.
The magnetic field is
concentrated in the core, which
extends into the secondary, so
the secondary intercepts more
field change.
The galvanometer will show
greater surges of current when
the switch of the primary is
opened or closed.
37.5 Transformers
37 Electromagnetic Induction
Instead of opening and closing a switch to produce the
change of magnetic field, an alternating current can
power the primary.
Then the rate of magnetic field changes in the primary
(and in the secondary) is equal to the frequency of the
alternating current.
Now we have a transformer, a device for increasing or
decreasing voltage through electromagnetic induction.
37.5 Transformers
37 Electromagnetic Induction
If the iron core forms a complete loop, guiding all
magnetic field lines through the secondary, the
transformer is more efficient.
All the magnetic field lines within the primary are
intercepted by the secondary.
37.5 Transformers
37 Electromagnetic Induction
Voltage
Voltages may be stepped up or stepped down with a
transformer.
Suppose the primary consists of one loop connected to a
1-V alternating source.
• Consider the arrangement of a one-loop secondary
that intercepts all the changing magnetic field lines
of the primary.
• Then a voltage of 1 V is induced in the secondary.
37.5 Transformers
37 Electromagnetic Induction
If another loop is wrapped around the core, the
induced voltage will be twice as much, in accord
with Faraday’s law.
If the secondary has a hundred times as many turns
as the primary, then a hundred times as much
voltage will be induced.
This arrangement of a greater number of turns on
the secondary than on the primary makes up a step-
up transformer.
Stepped-up voltage may light a neon sign or
operate the picture tube in a television receiver.
37.5 Transformers
37 Electromagnetic Induction
a. 1 V induced in the secondary equals the voltage of the primary.
37.5 Transformers
37 Electromagnetic Induction
a. 1 V induced in the secondary equals the voltage of the primary.
b. 1 V is induced in the added secondary also because it intercepts the
same magnetic field change from the primary.
37.5 Transformers
37 Electromagnetic Induction
a. 1 V induced in the secondary equals the voltage of the primary.
b. 1 V is induced in the added secondary also because it intercepts the
same magnetic field change from the primary.
c. 2 V is induced in a single two-turn secondary.
37.5 Transformers
37 Electromagnetic Induction
If the secondary has fewer turns than the primary, the
alternating voltage in the secondary will be lower than that in
the primary.
The voltage is said to be stepped down.
If the secondary has half as many turns as the primary, then
only half as much voltage is induced in the secondary.
37.5 Transformers
37 Electromagnetic Induction
The relationship between primary and secondary voltages with
respect to the relative number of turns is
37.5 Transformers
37 Electromagnetic Induction
A practical transformer uses many coils. The relative
numbers of turns in the coils determines how much the
voltage changes.
37.5 Transformers
37 Electromagnetic Induction
Power
You don’t get something for nothing with a transformer that
steps up the voltage, for energy conservation is always in
control.
The transformer actually transfers energy from one coil to the
other. The rate at which energy is transferred is the power.
The power used in the secondary is supplied by the primary.
37.5 Transformers
37 Electromagnetic Induction
The primary gives no more power than the secondary uses.
If the slight power losses due to heating of the core are
neglected, then the power going in equals the power
coming out.
Electric power is equal to the product of voltage and current:
(voltage × current)primary = (voltage × current)secondary
37.5 Transformers
37 Electromagnetic Induction
If the secondary has more
voltage, it will have less current
than the primary.
If the secondary has less
voltage, it will have more
current than the primary.
37.5 Transformers
37 Electromagnetic Induction
This transformer lowers 120 V to
6 V or 9 V. It also converts AC to
DC by means of a diode that acts
as a one-way valve.
37.5 Transformers
37 Electromagnetic Induction
think! When the switch of the primary is opened or
closed, the galvanometer in the secondary
registers a current. But when the switch remains
closed, no current is registered on the
galvanometer of the secondary. Why?
37.5 Transformers
37 Electromagnetic Induction
think! When the switch of the primary is opened or
closed, the galvanometer in the secondary
registers a current. But when the switch remains
closed, no current is registered on the
galvanometer of the secondary. Why?
Answer:
A current is only induced in a coil when there is a
change in the magnetic field passing through it.
When the switch remains in the closed position,
there is a steady current in the primary and a
steady magnetic field about the coil.
37.5 Transformers
37 Electromagnetic Induction
think! If the voltage in a transformer is stepped up, then the current is
stepped down. Ohm’s law says that increased voltage will produce
increased current. Is there a contradiction here, or does Ohm’s Law
not apply to transformers?
37.5 Transformers
37 Electromagnetic Induction
think! If the voltage in a transformer is stepped up, then the current is
stepped down. Ohm’s law says that increased voltage will produce
increased current. Is there a contradiction here, or does Ohm’s Law
not apply to transformers?
Answer:
Ohm’s law still holds, and there is no contradiction. The voltage
induced across the secondary circuit, divided by the load
(resistance) of the secondary circuit, equals the current in the
secondary circuit. The current is stepped down in comparison with
the larger current that is drawn in the primary circuit.
37.5 Transformers
37 Electromagnetic Induction
How does a transformer work?
37.5 Transformers
37 Electromagnetic Induction
Almost all electric energy sold today is in the
form of alternating current because of the ease
with which it can be transformed from one
voltage to another.
37.6 Power Transmission
37 Electromagnetic Induction
Power is transmitted great
distances at high voltages and
correspondingly low currents.
This reduces energy losses
due to the heating of the wires.
Power may be carried from
power plants to cities at about
120,000 volts or more, stepped
down to about 2400 volts in the
city, and finally stepped down
again to 120 volts.
37.6 Power Transmission
37 Electromagnetic Induction
Power transmission uses transformers to increase voltage for
long-distance transmission and decrease it before it reaches
your home.
37.6 Power Transmission
37 Electromagnetic Induction
Energy, then, is transformed from
one system of conducting wires
to another by electromagnetic
induction.
The same principles account for
sending energy from a radio-
transmitter antenna to a radio
receiver many kilometers away.
The effects of electromagnetic
induction are very far-reaching.
37.6 Power Transmission
37 Electromagnetic Induction
Why is almost all electrical energy sold today in
the form of alternating current?
37.6 Power Transmission
37 Electromagnetic Induction
A magnetic field is created in any region of space in
which an electric field is changing with time.
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
Electromagnetic induction has thus far been discussed in
terms of the production of voltages and currents.
The more fundamental way to look at it is in terms of the
induction of electric fields.
The electric fields, in turn, give rise to voltages and currents.
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
Induction takes place whether or not a conducting wire or
any material medium is present.
Faraday’s law states that an electric field is created in
any region of space in which a magnetic field is changing
with time.
The magnitude of the created electric field is proportional
to the rate at which the magnetic field changes.
The direction of the created electric field is at right angles
to the changing magnetic field.
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
If electric charge happens to be present where the
electric field is created, this charge will experience a
force.
• For a charge in a wire, the force could cause it to
flow as current, or to push the wire to one side.
• For a charge in the chamber of a particle
accelerator, the force can accelerate the charge to
high speeds.
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
There is a second effect, which is
the counterpart to Faraday’s law.
It is just like Faraday’s law, except
that the roles of electric and
magnetic fields are interchanged.
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
A magnetic field is created in any region of space in
which an electric field is changing with time.
• The magnitude of the magnetic field is proportional
to the rate at which the electric field changes.
• The direction of the created magnetic field is at
right angles to the changing electric field.
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
How can an electric field
create a magnetic field?
37.7 Induction of Electric and Magnetic Fields
37 Electromagnetic Induction
An electromagnetic wave is composed of
oscillating electric and magnetic fields that
regenerate each other.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
Shake the end of a stick back and forth in still water and you
will produce waves on the water surface.
Similarly shake a charged rod back and forth in empty space
and you will produce electromagnetic waves in space.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
The shaking charge can be considered an electric current.
• A magnetic field surrounds an electric current.
• A changing magnetic field surrounds a changing
electric current.
• A changing magnetic field creates a changing electric
field.
• The changing electric field creates a changing
magnetic field.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
An electromagnetic wave is composed of oscillating electric and magnetic fields that
regenerate each other.
No medium is required. The oscillating fields emanate from the vibrating charge.
At any point on the wave, the electric field is perpendicular to the magnetic field.
Both are perpendicular to the direction of motion of the wave.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
Speed of Electromagnetic Waves
For electromagnetic radiation, there is only
one speed—the speed of light—no matter
what the frequency or wavelength or intensity
of the radiation.
The changing electric field induces a
magnetic field. The changing magnetic field
acts back to induce an electric field.
Only one speed could preserve this
harmonious balance of fields.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
If the wave traveled at less than the speed of light, the fields
would rapidly die out.
The electric field would induce a weaker magnetic field, which
would induce a still weaker electric field.
If the wave traveled at more than the speed of light, the fields
would build up in a crescendo of ever greater magnitudes.
At some critical speed, however, mutual induction continues
indefinitely, with neither a loss nor a gain in energy.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
From his equations of electromagnetic induction,
Maxwell calculated the value of this critical speed
and found it to be 300,000 kilometers per second.
He used only the constants in his equations
determined by simple laboratory experiments with
electric and magnetic fields.
He didn’t use the speed of light. He found the speed
of light!
37.8 Electromagnetic Waves
37 Electromagnetic Induction
Nature of Light
Maxwell quickly realized that he had discovered the
solution to one of the greatest mysteries of the
universe—the nature of light.
Maxwell realized that radiation of any frequency would
propagate at the same speed as light.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
This radiation includes radio waves, which can be
generated and received by antennas.
• A rotating device in the sending antenna alternately
charges the upper and lower parts of the antenna
positively and negatively.
• The charges accelerating up and down the antenna
transmit electromagnetic waves.
• When the waves hit a receiving antenna, the electric
charges inside vibrate in rhythm with the variations of
the field.
37.8 Electromagnetic Waves
37 Electromagnetic Induction
What makes up an
electromagnetic wave?
37.8 Electromagnetic Waves
37 Electromagnetic Induction
1. A voltage will be induced in a wire loop when the magnetic field within
that loop
a. changes.
b. aligns with the electric field.
c. is at right angles to the electric field.
d. converts to magnetic energy.
Assessment Questions
37 Electromagnetic Induction
1. A voltage will be induced in a wire loop when the magnetic field within
that loop
a. changes.
b. aligns with the electric field.
c. is at right angles to the electric field.
d. converts to magnetic energy.
Answer: A
Assessment Questions
37 Electromagnetic Induction
2. If you change the magnetic field in a closed loop of wire, you induce in
the loop a
a. current.
b. voltage.
c. electric field.
d. all of these
Assessment Questions
37 Electromagnetic Induction
2. If you change the magnetic field in a closed loop of wire, you induce in
the loop a
a. current.
b. voltage.
c. electric field.
d. all of these
Answer: D
Assessment Questions
37 Electromagnetic Induction
3. The essential concept in an electric motor and a generator is
a. Coulomb’s law.
b. Ohm’s law.
c. Faraday’s law.
d. Newton’s second law.
Assessment Questions
37 Electromagnetic Induction
3. The essential concept in an electric motor and a generator is
a. Coulomb’s law.
b. Ohm’s law.
c. Faraday’s law.
d. Newton’s second law.
Answer: C
Assessment Questions
37 Electromagnetic Induction
4. A motor and a generator are
a. similar devices.
b. very different devices with different applications.
c. only found in hybrid cars.
d. energy sources.
Assessment Questions
37 Electromagnetic Induction
4. A motor and a generator are
a. similar devices.
b. very different devices with different applications.
c. only found in hybrid cars.
d. energy sources.
Answer: A
Assessment Questions
37 Electromagnetic Induction
5. A step-up transformer in an electrical circuit can
a. increase voltage.
b. decrease energy.
c. increase current.
d. increase energy.
Assessment Questions
37 Electromagnetic Induction
5. A step-up transformer in an electrical circuit can
a. increase voltage.
b. decrease energy.
c. increase current.
d. increase energy.
Answer: A
Assessment Questions
37 Electromagnetic Induction
6. To keep heat losses down when power is carried across the
countryside, it is best that current in the wires is
a. low.
b. high.
c. not too low and not too high.
d. replaced with voltage.
Assessment Questions
37 Electromagnetic Induction
6. To keep heat losses down when power is carried across the
countryside, it is best that current in the wires is
a. low.
b. high.
c. not too low and not too high.
d. replaced with voltage.
Answer: A
Assessment Questions
37 Electromagnetic Induction
7. According to James Clerk Maxwell, if the magnitude of the created magnetic
field increases, the change in the electric field will
a. stay the same.
b. increase.
c. decrease.
d. always disappear.
Assessment Questions
37 Electromagnetic Induction
7. According to James Clerk Maxwell, if the magnitude of the created magnetic
field increases, the change in the electric field will
a. stay the same.
b. increase.
c. decrease.
d. always disappear.
Answer: B
Assessment Questions
37 Electromagnetic Induction
8. Electricity and magnetism connect to form
a. mass.
b. energy.
c. ultra high-frequency sound.
d. light.
Assessment Questions
37 Electromagnetic Induction
8. Electricity and magnetism connect to form
a. mass.
b. energy.
c. ultra high-frequency sound.
d. light.
Answer: D
Assessment Questions