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Physics / Higher Physics 1B

Electricity and Magnetism

Part II Administrative Detailsn Michael Ashley

n Room 129, OMB

n My course website: http://mcba11.phys.unsw.edu.au/~mcba/PHYS1231

n Please collect homework books from 1st Year Lab

n Please bring your lab book next week

n Blackboard site for course information:

n http://lms-blackboard.telt.unsw.edu.au

n Lecture Notesn ppt slides + movies

n Also Richard Newbury’s (excellent!) notes

n Tutorial solutions

n Multiple Choice quizzes

n Ancillary informationn Administration, syllabus, on-line study, academic honesty

Assessment

n Laboratory 20%

n Six quizzes 20%

n End of Session exam 60%

n You must pass each component and complete all the labs

Syllabus

n Electrostatics (§23.1, 23.3-23.6)

n Gauss’s Law (§24.1-24.3)

n Electric Potential (§25.1-25.6)

n Capacitance & Dielectrics (§26.1-26.5)

n Magnetic Fields & Magnetism (§29.1-29.3)

n Ampere’s & Biot-Savart Law (§30.1-30.5)

n Faraday’s Law, Induction, Inductance (§31.1-

31.6, 32.1-32.3)

Chapter 23

Electric Fields

2

Electricity and Magnetism,

Some Ancient History

n Many applications

n Macroscopic and microscopic

n Chinese

n Documents suggest that magnetism was observed

as early as 2000 BC

n Greeks

n Electrical and magnetic phenomena as early as

700 BC

n Experiments with amber and magnetite

Electricity and Magnetism,

Some History, 2

n 1785

n Charles Coulomb confirmed inverse

square law form for electric forces

n 1819

n Hans Oersted found a compass needle

deflected when near a wire carrying an

electric current

Electricity and Magnetism,

Some History, 3

n 1831

n Michael Faraday and Joseph Henry showed that when a wire is moved near a magnet, an electric current is produced in the wire

n 1873

n James Clerk Maxwell used observations and other experimental facts as a basis for formulating the laws of electromagnetism

n Unified electricity and magnetism

Electric Charges, 1

n There are two kinds of electric charges

n Called positive and negative

n Negative charges are the type possessed by electrons

n Positive charges are the type possessed by protons

n Charges of the same sign repel one another and charges with opposite signs attract one another

Charges in matter: the atom

n EFA02AN1

Demo EA3: Electrostatic forces

n Attraction of a stream of water by a charged rod

3

Demo EA1: Electrostatic Charging by Friction – can move large objects

Glass rubbed with silk will gain a positive charge and plastic rubbed with fur a negative charge. A metal rod will also acquire a charge if rubbed with rubber and held by an insulated handle.

Electric Charges, 2

n The rubber rod is

negatively charged

n The glass rod is

positively charged

n The two rods will

attract

Electric Charges, 3

n The rubber rod is

negatively charged

n The second rubber

rod is also

negatively charged

n The two rods will

repel

More About Electric Charges

n Electric charge is always conserved in

an isolated system

n For example, charge is not created in the

process of rubbing two objects together

n The electrification is due to a transfer of

charge from one object to another

Conservation of Electric

Charges

n A glass rod is rubbed

with silk

n Electrons are

transferred from the

glass to the silk

n Each electron adds a

negative charge to the

silk

n An equal positive

charge is left on the rod

Quantization of Electric

Charges

n The electric charge, q, is said to be quantized

n q is the standard symbol used for charge

n Electric charge exists as discrete packets

n q = Ne

n N is an integer

n e is the fundamental unit of charge

n |e| = 1.6 x 10-19 C

n Electron: q = -e

n Proton: q = +e

4

Conductors

n Electrical conductors are materials in which some of the electrons are free electrons

n Free electrons are not bound to the atoms

n These electrons can move relatively freely through the material

n Examples of good conductors include copper, aluminum and silver

n When a good conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material

Insulators

n Electrical insulators are materials in which all of the electrons are bound to atoms

n These electrons cannot move freely through the material

n Examples of good insulators include glass, rubber and wood

n When a good insulator is charged in a small region, the charge is unable to move to other regions of the material

Semiconductors

n The electrical properties of

semiconductors are somewhere

between those of insulators and

conductors

n Examples of semiconductor materials

include silicon and germanium

Quick Quiz 23.2

Three objects are brought close to each other, two at a time.

When objects A and B are brought together, they repel.

When objects B and C are brought together, they also repel.

Which of the following are true?

(a) Objects A and C possess charges of the same sign.

(b) Objects A and C possess charges of opposite sign.

(c) All three of the objects possess charges of the same sign.

(d) One of the objects is neutral.

(e) We would need to perform additional experiments to

determine the signs of the charges.

Answer: (a), (c), and (e). The experiment shows that A and

B have charges of the same sign, as do objects B and C.

Thus, all three objects have charges of the same sign. We

cannot determine from this information, however, whether

the charges are positive or negative.

Quick Quiz 23.2 Conductors - charge distribution

n EFM03VD2

5

Coulomb�s Law

n Charles Coulomb

measured the

magnitudes of electric

forces between two

small charged spheres

n He found the force

depended on the

charges and the

distance between them

Coulomb�s Law, Equation

n Mathematically,

n The SI unit of charge is the Coulomb (C)

n ke is called the Coulomb constant

n ke = 8.9875 x 109 N.m2/C2 = 1/(4πεo)

n εo is the permittivity of free space

n εo = 8.8542 x 10-12 C2 / N.m2

Fe = ke

q1q2

r2

Coulomb’s Law

n EFM04AN1

Coulomb�s Law

n The force is attractive if the charges are of opposite sign

n The force is repulsive if the charges are of like sign

n The electrical behavior of electrons and protons is well described by modelling them as point charges

n The electrical force is a �conservative� forcen i.e. the same work is done whatever path is taken to

move between two positions

Fe = ke

q1q2

r2

Coulomb's Law, Notes

n Remember the charges need to be in Coulombs

n e is the smallest unit of chargen [except quarks� .]

n e = 1.6 x 10-19 C

n So 1 C needs 1/e = 6.24 x 1018 electrons or protons!

n Typical charges can be in the µC range

n Remember that force is a vector quantity

Demo Ea2: Electrostatic forces

6

Vector Nature of Electric

Forces

n In vector form,

n is a unit vector

directed from q1 to q2

n Like charges produce a

repulsive force between

them

F12 = ke

q1q2

r2� r

� r

Vector Nature of Electrical

Forces, 2

n Electrical forces obey Newton�s Third

Law

n The force on q1 is equal in magnitude and

opposite in direction to the force on q2

n F21 = -F12

n With like signs for the charges, the

product q1q2 is positive and the force is

repulsive

Vector Nature of Electrical

Forces, 3

n Two point charges are

separated by a

distance r

n With unlike signs for

the charges, the

product q1q2 is

negative and the force

is attractive

Quick Quiz 23.4

Object A has a charge of +2 µC, and object B has a charge of

+6 µC. Which statement is true about the electric forces on

the objects?

(a) FAB = �3FBA

(b) FAB = �FBA

(c) 3FAB = �FBA

(d) FAB = 3FBA

(e) FAB = FBA

(f) 3FAB = FBA

Answer: (e). From Newton's third law, the electric force

exerted by object B on object A is equal in magnitude to the

force exerted by object A on object B.

Quick Quiz 23.4 Quick Quiz 23.5

Object A has a charge of +2 µC, and object B has a charge of

+6 µC. Which statement is true about the electric forces on

the objects?

(a) FAB = �3FBA

(b) FAB = �FBA

(c) 3FAB = �FBA

(d) FAB = 3FBA

(e) FAB = FBA

(f) 3FAB = FBA

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Answer: (b). From Newton's third law, the electric force

exerted by object B on object A is equal in magnitude to the

force exerted by object A on object B and in the opposite

direction.

Quick Quiz 23.5

Hydrogen Atom Example

n The electrical force between the electron and

proton is found from Coulomb�s law

n Fe = keq1q2 / r2 = 8.2 x 10-8 N (exercise� .)

n This can be compared to the gravitational

force between the electron and the proton

n Fg = Gmemp / r2 = 3.6 x 10-47 N (exercise� )

n The electric force is vastly stronger than the

gravitational force!

QuickTime™ and aGraphics decompressor

are needed to see this picture.

Strength Electrostatic Forces c.f. Gravity

n EFA04AN1

The Superposition Principle

n The resultant force on any one charge

equals the vector sum of the forces

exerted by the other individual charges

that are present

n The resultant force on q1 is the vector

sum of all the forces exerted on it by

other charges: F1 = F21 + F31 + F41 + �

Superposition Principle,

Example

n The force exerted by

q1 on q3 is F13

n The force exerted by

q2 on q3 is F23

n The resultant force

exerted on q3 is the

vector sum of F13 and

F23

Example

n Calculate the force for charges +q, +Q and -Q, distributed at the vertices of an equilateral triangle.

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Electrical Force with

Gravitational Force; example

n The spheres are in

equilibrium

n Since they are separated,

they exert a repulsive

force on each other

n Like charges

n Equate the forces, since

they are in equilibrium

n note that one force is an

electrical force and the

other is gravitational

Electrical Force with

Gravitational Forces; example

n The free body diagram includes the components of the tension, the electrical force, and the weight

n Solve for |q|

n You cannot determine the sign of q, only that they both have same sign

Demo EA5: Electrostatic field and lines of force

n Paper strips attached to a van der Graaf generator show the electrostatic field lines; i.e. the direction of the electric field.

n Think about the inverse square law:n the number of lines per

unit area.

Electric Field �Definition

n An electric field is said to exist in the

region of space around a charged

object

n This charged object is the source charge

n When another charged object, the test

charge, enters this electric field, an

electric force acts on it

Electric Field �Definition, cont

n The electric field is defined as the electric

force on the test charge per unit charge

n The electric field vector, E, at a point in space

is defined as the electric force F acting on a

positive test charge, qo placed at that point

divided by the test charge: E = Fe / qo.

n i.e. Fe = q0 E

n Strictly, only valid for a point charge

Electric Field Notes, Final

n The direction of E is that of the force on a positive test charge

n The SI units of E are N/C

n We can also say that an electric field exists at a point in space if a test charge at that point experiences an electric force

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Electric Field, Vector Form

n Remember Coulomb�s law, between the

source and test charges, can be

expressed as

n Then, the electric field will be

2�o

e e

qqk

r=F r

2�e

e

o

qk

q r= =F

E r

Superposition with Electric

Fields

n At any point P, the total electric field due

to a group of source charges equals the

vector sum of electric fields of all the

charges

2�i

e i

i i

qk

r= ∑E r

Superposition Example

n Find the electric field at point P due to q1, E1

n Find the electric field at point P due to q2, E2

n E = E1 + E2

n Remember, the fields add as vectors

n The direction of the individual fields is the direction of the force on a positive test charge

Electric Field �Continuous

Charge Distribution

n Divide the charge

distribution into small

elements, each of which

contains �q

n Calculate the electric field

due to one of these

elements at point P

n Evaluate the total field by

summing the contributions

of all the charge elements

Electric Field �Continuous

Charge Distribution, equations

n For the individual charge elements

n Because the charge distribution is

continuous

2�

e

qk

r

∆∆ =E r

2 20� �lim

i

ie i e

qi i

q dqk k

r r∆ →

∆= =∑ ∫E r r

Charge Densities

n Volume charge density: when a charge is distributed evenly throughout a volume

n ρ = Q / V

n Surface charge density: when a charge is distributed evenly over a surface area

n σ = Q / A

n Linear charge density: when a charge is distributed along a linen λ = Q / ℓ

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Example �Charged Disk

n The ring has a radius R

and a uniform charge

density σ

n Choose dq as a ring of

radius r

n The ring has a surface

area 2πr dr

n Calculate E-field at P a

distance x away on axis

n Example 23.9

Electric Field Lines

n Field lines give us a means of representing the electric field pictorially

n The electric field vector E is tangent to the electric field line at each pointn The line has a direction that is the same as that of

the electric field vector

n The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region

Electric Field Lines, General

n The density of lines through surface A is greater than through surface B

n The magnitude of the electric field is greater on surface A than B

n The lines at different locations point in different directionsn This indicates the field is

non-uniform

Electric Field: van der Graaf generator

n EFM05VD1

Demo EA14: van der Graaf generator

n Electric field, and lines of force, shown in a hair-raising experiment!

n With clean hair, the subject’s hair will stand on end as it becomes charged.

Electric Field Lines, Positive

Point Charge

n The field lines radiate

outward in all directionsn In three dimensions, the

distribution is spherical

n The lines are directed

away from the source

chargen A positive test charge would

be repelled away from the positive source charge

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Electric Field Lines, Negative

Point Charge

n The field lines radiate

inward in all directions

n The lines are directed

toward the source

charge

n A positive test charge

would be attracted

toward the negative

source charge

Electric Field Lines �Dipole

n The charges are

equal and opposite

n The number of field

lines leaving the

positive charge

equals the number

of lines terminating

on the negative

charge

Electric Field Lines �Like

Charges

n The charges are equal and positive

n The same number of lines leave each charge since they are equal in magnitude

n At a great distance, the field is approximately equal to that of a single charge of 2q

Quick Quiz 23.7

Rank the magnitude of the electric field at points A, B, and C

shown in this figure (greatest magnitude first).

(a) A, B, C

(b) A, C, B

(c) B, C, A

(d) B, A, C

(e) C, A, B

(f) C, B, A

Answer: (a). The field is greatest at point A because this is

where the field lines are closest together. The absence of

lines near point C indicates that the electric field there is

zero.

Quick Quiz 23.7 Quick Quiz 23.8

Which of the following statements about electric field lines

associated with electric charges is false?

(a) Electric field lines can be either straight or curved.

(b) Electric field lines can form closed loops.

(c) Electric field lines begin on positive charges and end on

negative charges.

(d) Electric field lines can never intersect with one another.

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Answer: (b). Electric field lines begin and end on charges

and cannot close on themselves to form loops.

Quick Quiz 23.8

Motion of Charged Particles

n When a charged particle is placed in an electric field, it experiences an electrical force

n If this is the only force on the particle, it must be the net force

n The net force will cause the particle to accelerate according to Newton�s second law

Motion of Particles, cont

n Fe = qE = ma

n If E is uniform, then a is constant

n If the particle has a positive charge, its

acceleration is in the direction of the

field

Electron in a Uniform Field,

Example

n The electron is projected

horizontally into a uniform

electric field

n The electron undergoes a

downward acceleration

n It is negative, so the

acceleration is opposite E

n F=ma=qE so that a=qE/m

n Its motion is parabolic while

between the plates

n c.f. projectile motion under gravity

End of Chapter

Quick Quiz 23.1

If you rub an inflated balloon against your hair, the two

materials attract each other, as shown in this figure. Fill in

the blank: the amount of charge present in the system of the

balloon and your hair after rubbing is _____ the amount of

charge present before rubbing.

(a) less than

(b) the same as

(c) more than

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Answer: (b). The amount of charge present in the isolated

system after rubbing is the same as that before because

charge is conserved; it is just distributed differently.

Quick Quiz 23.1 Quick Quiz 23.6

A test charge of +3 µC is at a point P where an external

electric field is directed to the right and has a magnitude of 4

× 106 N/C. If the test charge is replaced with another test

charge of �3 µC, the external electric field at P

(a) is unaffected

(b) reverses direction

(c) changes in a way that cannot be determined

Answer: (a). There is no effect on the electric field if we

assume that the source charge producing the field is not

disturbed by our actions. Remember that the electric field is

created by source charge(s) (unseen in this case), not the test

charge(s).

Quick Quiz 23.6