1

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2. Access to

Required items:

FRETWELLSPRING2017

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(for the online homework)

Physics: Principles with Applications, 7th ed, Vol 2. by Giancoli.

Available in printed form or as an eBook with Mastering Physics

Electric Charge• Its Conservation• In the Atom• Insulators and Conductors• Induced Charge • Electroscope

Electric ForceCoulomb’s Law

Electric Field• Field Lines• E fields and conductors• Gauss’s Law

16.1 Static Electricity; Electric Charge and Its Conservation

-+

Charge comes in two types: + and -

Objects can be

charged by rubbing

(which moves electrons from one object to the other)

Human skin

Rabbit's fur

Glass

Human hair

Nylon

Wool

Lead

Cat's fur

Silk

Aluminium

Paper (Small positive charge)

Cotton (No charge)

Steel (No charge)

Wood (Small negative charge)

Amber

Polystyrene

Rubber balloon

Brass

Gold

Synthetic rubber

Styrofoam

Plastic wrap

Scotch tape

PVC

rubber

Triboelectric series

Most

positively

charged

Most

negatively

charged

0

+

-

Electric charge is an intrinsic property

of some elementary particles

A negatively negatively negatively negatively charged object has an excess of - charge

A positively positively positively positively charged object has lost some of its - charge

Net chargeNet chargeNet chargeNet charge = sum of all + and - charges in an object

FFFFree charges ree charges ree charges ree charges are loosely bound electrons that can move freely around a conductor

A neutralneutralneutralneutral object has equal amounts of + and - charge

[not for the exam]

Static Electricity; Electric Charge and Its Conservation

Like charges repel

i.e. the net charge

produced in any

process is zero

Opposite charges attract.

+---

Electric charge is conserved

In a conductor (e.g. a metal), charge flows freely

Almost no charge flows in an insulator

Semiconductors (e.g. Si) have an intermediate

conductivity

16.4 Induced Charge

or by induction.

Charge is induced at each

end of the metal rod.

We can see induction inconductors because it gives riseto a net attractive interaction

+

+ -

Metal objects can be charged by conduction,

Neutral metal rod acquires a charge when

it is touched by a charged metal object.

2

To get a permanent charge on the metal rod by inductiona path must be provided for charge to flow …

Induced Charge

Cut the wire with the charged object nearby.

The rod is now permanentlycharged. It has the opposite charge

to the original charged object.

electrophorus

Ground or Earth

= reservoir where charge moves freely to/from

Induced Charge

Charge separation can also be induced inside the atoms or molecules of a nonconductor where it again gives rise to a

… so balloons stick to walls.

weak attractive interaction

Atom or molecule

The Electroscope

A charged electroscope can be used to determine the sign of an unknown charge.

Same chargeLeaves open more

Opposite chargeLeaves close

Then bring the unknown charge

close to the electroscope.First charge it by

induction or conduction.

A metal ball hangs from the ceilingby an insulating thread. The ball isattracted to a positive-charged rodheld near the ball.

The charge of the ball must be:

1. Only positive

2. Only negative

3. Only neutral

4. Positive or neutral

5. Negative or neutral

Question

16.5 Coulomb’s Law

The magnitude of the electric force between two point charges is

proportional to the product of the charges and inversely proportional to the square of the distance between them.

Units = Coulomb

(16-1)

k = 8.988 × 109 Nm2/C2

Insignificant volume

Units of charge = Coulomb, C

k can also be written in terms of εεεε0, the permittivity of free permittivity of free permittivity of free permittivity of free spacespacespacespace

The electric force is typically much stronger than the gravitational force

aka Electric constantElectric constantElectric constantElectric constant

�� =1

4��= 8.85 × 10 !" #"/%&"

Coulomb’s Law

Force acts along the line connecting the charges.

repel

attract

Same charges

Opposite charges

force on 1 due to 2

force on 2 due to 1

Which charge feels the

bigger force?

+ 1C + 2 C

Question

3

Coulomb’s Law

All electrons have the same charge:

Smallest isolated charge found in nature

Electric charge is quantized in units of the electron charge, e.

~ 1013 electrons

Charges produced by rubbing are

typically around a microcoulomb: ~ 10-6 C

Magnitude of resultant force is,above the

+x axis' = '(" + '*

"+ = ,-. !

'*

'(

+

+

140 N 850 N−−−− x

y

10o

40o

'( = 850 cos 10 − 140 cos(50)

'* = 850 sin 10 + 140 sin(50)And the direction is given by,

θ

Take care when working in other quadrants

To calculate the Net Force on a charge…

Example: What is the

net force acting on the negative charge?

Force is a vector quantity

1. Draw a picture and roughly determine the net force2. Calc. the components of force acting on a charge due to all other charges

3. Add the x and y components of the forces separately:

16.7 The Electric Field

Electric field is defined to be the force felt by a smallpositive ‘test’ charge, q, divided by that charge:

(16-3)

Units N/CSmall enough not to disturb charges that created E

… it depends on the charges that produce the electric field.Note, E does not depend on q …

If q is positive, E and F point

in the same direction

If q is negative, E and F point

in opposite directions

Near a Uranium nucleus92 protons

3 x 1021 N/C

5 x 1011 N/C

3,000,000 N/C+

+

+

+ +++

++

++

+

++

+

++

+

++

++

+

+proton

electron

+

~150N/C

Near a comb

~1000 N/C

Inside a

hydrogen atom

-

Near the Earth’s surface

Electrical

breakdown in air

How big are the Electric fields around us?

Electric Field

Electric field (like force) is a vector.

Components can be added to give the net electric field at a point

+ -

E is a vector that points away from (+) charges...

… and towards (-) charges

For a point charge:

(16-4a)

[magnitude]

A small −−−− 4.0 µµµµC charge sits in auniform electric field and feels adownward (electric) force of 6.0 N.

F = 6.0 N

- 4.0 µµµµC

1. 1.5 x 106 N/C UP

2. 1.5 x 106 N/C DOWN

3. 6.7 x 10-7 N/C UP

4. 6.7 x 10-7 N/C DOWN

5. E = kQ/r2

What is the electric field at this point (ignore gravity) ?

Question

4

The Electric Field

Problem solving in electrostatics:

Electric forces and electric fields

(show all charges with signs, and fields and forces with directions)

2. Calculate all components of forces or fields.

' =23435

65; or 7 =

23

65 for point charges

3. Add forces or fields vector components to get resultant.

1. Draw a diagram.

Example. Calculate the electric field near a dipole

Field at B: E1= (9x109)(50x10-6)/.3972 = 2.86x106 N/C

x y

E1 2.86x106cos49 2.86x106sin49

E2 2.86x106cos49 - 2.86x106sin49

Add x and y components:

E2 = (9x109)(50x10-6)/.3972 = 2.86x106 N/C

30 cm

21

+50 µC -50 µC

B

26 cm

49o

49o

7 = ( 3.75 × 10: " + 0")

= 3.75 × 10: %/#

From geometry, and are 49o

above and below the horizontal

7!

7"

7! 7"

In the +x direction.

7

E 3.75x106 0

30 cm

21

+50 µC -50 µC

B

Example. Calculate the electric field near a dipole

26 cm

49o

49o

OR - Use the symmetry:

E = 2 E1 cos49

Generally,

Sum of any 2 vectors of equal

magnitude is

θθ

and have same magnitude

7!

7! 7"

7"

So we can immediately write down the answer…

= 3.75 × 10: %/#

In the +x direction.

E = 2 E1 cosθ

7!

7"

½ the angle

between the

2 vectors

7

Is there a point on the line where E = 0?

-Q +2Q

What happens if a 3rd charge is placed at that point?

10 cm

What if the two charge have the same sign?

Question

16.8 Field Lines

The electric field can be represented by field lines.

E.g. Electric dipole(two opposite charges)

Electric field is stronger when the

field lines are closer together.

Field lines start on (+) charges

and end on (-) charges.

The field at a point is a vector tangential to the field

line there.

Field lines

never cross

Field Lines: near point charges

Two charges of the same magnitude and sign.

Two charges of different magnitude and opposite sign.

Where is E = 0 in these figures?

Electric dipole

Magnitude of point charge

∝∝∝∝ Number of field linesstarting/ending on that charge.

5

Field Lines: inside a capacitor

The electric field between twoclosely spaced, oppositely chargedparallel plates is UNIFORM

(same value everywhere)

Can be derived using Gauss’s Law.

(each plate carries charge Q and has area A)

Field lines are

equally spaced

7 =;

<��

= =>.?,-.,

If it were not, the charges inside the conductor would

feel a force and move around in order to make E zero.

Static electric field inside a solid conductor is zero

Any net charge in a conductor distributes itself on the surface.

E = 0

----

--------

------ - - - - -

Solid metal sphere with -Q

net charge

16.9 Electric Fields and Conductors

Electric field is perpendicular tothe outer surface of a conductor

E

– if it were not, charges would move to make it perpendicular.

E = 0inside

+Q

Inner surface -Q

Outer surface +Q

Neutral

conducting shell

Electric Fields and Conductors

What are some of the consequences of this ?

From the outside it looks as though the shell is not there

+Q

Neutral

conducting shell

If a point charge Q is placed at the center of a NEUTRAL hollow

conducting shell, the E field induces a separation of charge in the shell.

Electric Fields and Conductors

+3Q

−3Q appears on inner surface

+2Q appears on outer surface

Field lines radiate out from the central +3Q charge.

-Q

→

→

%@,=A-BC@>.?A@DD = ;inner + ;outer−; = −3; + ;outer

Now let the shell carry some charge..

E field outside shell is identical to one that would be produced

by a +2Q point charge, (= 3Q −Q) at the center of the shell

Shell has net charge of -Q.

A +3Q point charge is at the center of

hollow conducting spherical shell.

What is the charge on the

outer surface of the shell?

E field outside any charged spherical conductor (solid or hollow) is the same as if all the charge were concentrated at the center of the sphere.

Electric Fields and Conductors

Application: Faraday cage – used to shield people and equipment from external electric fields

16.12 Gauss’s Law

Electric flux

(16-7)

Electric flux through an area is proportional to the number of field lines crossing the area.

Introduce a new concept..

Gauss’s Law can be used to calculate E

Between 7 and area normal

6

Gauss’s Law

Total Flux through (an imaginary) closed surface,

Double charge enclosed → double the flux through

the closed surface

+

Net flux flows outof closed surface+

Zero flux flows through closed

surface

++

Flux in (left) = - Flux out (right)

Gauss’s Law

(16-9)

Gauss’s Law can be used to find the electric field in situations with a high degree of symmetry…

Total electric flux through closed surface

charge enclosed by closed surface

By convention, flux is positive if

it’s coming out of a closed surface

Gauss’s

Law

Total electric flux passing through a closed surface is proportional to the charge enclosed by that surface.

Ex.16-12. Calc. E field using Gauss’s Law for a charged metal shell of radius r0 with net charge Q.

so 7 = ;/4EF0B2

Charge enclosed by <2 = 0

So 7 = 0 0B<B01

E

rr0

~ 1/r2

Outside the shell: imagine a spherical closed surface, <1 0B H B01

0B H B01

Charge enclosed by <1= E Σ ∆A = E(4πr2)

A2

rr

A1

What if the shell was a solid sphere instead?

[there will be no derivations using Gauss’s Law in the Exam]

Inside the shell: imagine surface <2 0B I B01

Σ E⊥∆A = Q/ε0

E field outside a charged spherical shellis the same as if all the charge were

concentrated at the center of the shell.

So,

• Two kinds of electric charge – positive and negative

• Charge is conserved

• Charge on electron:

• Charge is quantized in units of e

• Conductors: electrons free to move

Summary of Chapter 16

• Objects can be charged by conduction or induction

• Coulomb’s law: Electric field is force per

unit charge:

• Electric field of a point charge, Q:

• Electric field can be represented by electric field lines

• Static electric field inside conductor is zero; surface field is perpendicular to surface

• Electric flux: Gauss’s law: