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Physics / Higher Physics 1B

Electricity and Magnetism

Administrative Details Michael Ashley, m.ashley@unsw.edu.au

Room 137, OMB

My course website (linked from “lecturer’s notes” in Moodle): http://mcba11.phys.unsw.edu.au/~mcba/PHYS1231

Please ensure you have a “course pack”

Please bring your lab book next week

Moodle site for course information:

http://moodle.telt.unsw.edu.au

Lecture Notes ppt slides + movies

Tutorial solutions

Multiple choice quizzes

Ancillary information Administration, syllabus, on-line study, academic honesty

Assessment

Laboratory 20%

Six quizzes 20% (due Sunday 11pm odd weeks; beginning week 3)

End of Session exam 60%

You must pass each component and complete all the labs

Syllabus (Physics for Scientists and Engineers with Modern Physics, Serway & Jewitt, 8th ed)

Electrostatics (§23.1, 23.3-23.6)

Gauss’s Law (§24.1-24.4)

Electric Potential (§25.1-25.6, 25.8)

Capacitance & Dielectrics (§26.1-26.5)

Magnetic Fields & Magnetism (§29.1-29.4)

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

Faraday’s Law, Induction, Inductance (§31.1-31.6, 32.1, 32.3)

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Chapter 23

Electrostatics

Before we get started… just for fun…

What would happen if you could throw a ball at 0.9c?

Electricity and Magnetism,

Some Ancient History

Many applications

Macroscopic and microscopic

Chinese

Documents suggest that magnetism was observed

as early as 2000 BC

Greeks

Electrical and magnetic phenomena as early as

700 BC

Experiments with amber and magnetite

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Electricity and Magnetism,

Some History, 2

1785

Charles Coulomb confirmed inverse

square law form for electric forces

1819

Hans Oersted found a compass needle

deflected when near a wire carrying an

electric current

Electricity and Magnetism,

Some History, 3

1831 Michael Faraday and Joseph Henry showed that

when a wire is moved near a magnet, an electric current is produced in the wire

1873 James Clerk Maxwell used observations and other

experimental facts as a basis for formulating the laws of electromagnetism

Unified electricity and magnetism

Electric Charges, 1

There are two kinds of electric charges

Called positive and negative Negative charges are the type possessed by

electrons

Positive charges are the type possessed by protons

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

Charges in matter: the atom

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Demo EA3: Electrostatic forces

Attraction of a stream of water by a charged rod

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

The rubber rod is

negatively charged

The glass rod is

positively charged

The two rods will

attract

Electric Charges, 3

The rubber rod is

negatively charged

The second rubber

rod is also

negatively charged

The two rods will

repel

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More About Electric Charges

Electric charge is always conserved in

an isolated system

For example, charge is not created in the

process of rubbing two objects together

The electrification is due to a transfer of

charge from one object to another

Conservation of Electric

Charges

A glass rod is rubbed

with silk

Electrons are

transferred from the

glass to the silk

Each electron adds a

negative charge to the

silk

An equal positive

charge is left on the rod

Quantization of Electric

Charges

The electric charge, q, is said to be quantized

q is the standard symbol used for charge

Electric charge exists as discrete packets

q = Ne

N is an integer

e is the fundamental unit of charge

|e| = 1.6 x 10-19 C

Electron: q = -e

Proton: q = +e

Conductors

Electrical conductors are materials in which some of the electrons are free electrons Free electrons are not bound to the atoms

These electrons can move relatively freely through the material

Examples of good conductors include copper, aluminum and silver

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

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Insulators

Electrical insulators are materials in which all of the electrons are bound to atoms These electrons cannot move freely through the

material

Examples of good insulators include glass, rubber and wood

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

Semiconductors

The electrical properties of

semiconductors are somewhere

between those of insulators and

conductors

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

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Conductors - charge distribution

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Coulomb’s Law

Charles Coulomb

measured the

magnitudes of electric

forces between two

small charged spheres

He found the force

depended on the

charges and the

distance between them

Coulomb’s Law, Equation

Mathematically,

The SI unit of charge is the Coulomb (C)

ke is called the Coulomb constant

ke = 8.9875 x 109 N.m2/C2 = 1/(4πo)

o is the permittivity of free space

o = 8.8542 x 10-12 C2 / N.m2

Fe k

e

q1q

2

r2

Coulomb’s Law

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Coulomb’s Law

The force is attractive if the charges are of opposite sign

The force is repulsive if the charges are of like sign

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

The electrical force is a “conservative” force i.e. the same work is done whatever path is taken to

move between two positions

Fe k

e

q1q

2

r2

Coulomb's Law, Notes

Remember the charges need to be in Coulombs e is the smallest unit of charge

[except quarks….]

e = 1.6 x 10-19 C

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

Typical charges can be in the µC range

Remember that force is a vector quantity

Demo Ea2: Electrostatic forces

Vector Nature of Electric

Forces

In vector form,

is a unit vector

directed from q1 to q2

Like charges produce a

repulsive force between

them

F12 k

e

q1q

2

r2

ˆ r

ˆ r

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Vector Nature of Electrical

Forces, 2

Electrical forces obey Newton’s Third

Law

The force on q1 is equal in magnitude and

opposite in direction to the force on q2

F21 = -F12

With like signs for the charges, the

product q1q2 is positive and the force is

repulsive

Vector Nature of Electrical

Forces, 3

Two point charges are

separated by a

distance r

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

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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

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

The electrical force between the electron and

proton is found from Coulomb’s law

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

This can be compared to the gravitational

force between the electron and the proton

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

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

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The Superposition Principle

The resultant force on any one charge

equals the vector sum of the forces

exerted by the other individual charges

that are present

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

The force exerted by

q1 on q3 is F13

The force exerted by

q2 on q3 is F23

The resultant force

exerted on q3 is the

vector sum of F13 and

F23

Example

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

Electrical Force with

Gravitational Force; example

The spheres are in

equilibrium

Since they are separated,

they exert a repulsive

force on each other

Like charges

Equate the forces, since

they are in equilibrium

note that one force is an

electrical force and the

other is gravitational

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Electrical Force with

Gravitational Forces; example

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

Solve for |q|

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

Demo EA5: Electrostatic field and lines of force

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

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

unit area.

Electric Field – Definition

An electric field is said to exist in the

region of space around a charged

object

This charged object is the source charge

When another charged object, the test

charge, enters this electric field, an

electric force acts on it

Electric Field – Definition, cont

The electric field is defined as the electric

force on the test charge per unit charge

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.

i.e. Fe = q0 E

Strictly, only valid for a point charge

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Electric Field Notes, Final

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

The SI units of E are N/C

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

Electric Field, Vector Form

Remember Coulomb’s law, between the

source and test charges, can be

expressed as

Then, the electric field will be

2ˆo

e e

qqk

rF r

2ˆe

e

o

qk

q r

FE r

Superposition with Electric

Fields

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

2ˆi

e i

i i

qk

r E r

Superposition Example

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

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

E = E1 + E2 Remember, the fields add

as vectors

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

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Electric Field – Continuous

Charge Distribution

Divide the charge

distribution into small

elements, each of which

contains Δq

Calculate the electric field

due to one of these

elements at point P

Evaluate the total field by

summing the contributions

of all the charge elements

Electric Field – Continuous

Charge Distribution, equations

For the individual charge elements

Because the charge distribution is

continuous

2ˆ

e

qk

r

E r

2 20

ˆ ˆlimi

i

e i eq

i i

q dqk k

r r

E r r

Charge Densities

Volume charge density: when a charge is distributed evenly throughout a volume ρ = Q / V

Surface charge density: when a charge is distributed evenly over a surface area σ = Q / A

Linear charge density: when a charge is distributed along a line = Q / ℓ

Example – Charged Disk

The ring has a radius R

and a uniform charge

density σ

Choose dq as a ring of

radius r

The ring has a surface

area 2πr dr

Calculate E-field at P a

distance x away on axis

Example 23.9

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Electric Field Lines

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

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

the electric field vector

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

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

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

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

non-uniform

Electric Field: van der Graaf generator

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Demo EA14: van der Graaf generator

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

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

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Electric Field Lines, Positive

Point Charge

The field lines radiate

outward in all directions In three dimensions, the

distribution is spherical

The lines are directed

away from the source

charge A positive test charge would

be repelled away from the

positive source charge

Electric Field Lines, Negative

Point Charge

The field lines radiate

inward in all directions

The lines are directed

toward the source

charge

A positive test charge

would be attracted

toward the negative

source charge

Electric Field Lines – Dipole

The charges are

equal and opposite

The number of field

lines leaving the

positive charge

equals the number

of lines terminating

on the negative

charge

Electric Field Lines – Like

Charges

The charges are equal and positive

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

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

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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.

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

and cannot close on themselves to form loops.

Quick Quiz 23.8

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Motion of Charged Particles

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

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

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

Motion of Particles, cont

Fe = qE = ma

If E is uniform, then a is constant

If the particle has a positive charge, its

acceleration is in the direction of the

field

Electron in a Uniform Field,

Example

The electron is projected

horizontally into a uniform

electric field

The electron undergoes a

downward acceleration

It is negative, so the

acceleration is opposite E

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

Its motion is parabolic while

between the plates

c.f. projectile motion under

gravity

End of Chapter

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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

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