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Chapter 22: Electric Charge and Electric Field

Electric ChargeAncient Greeks ~ 600 BC Static electicity: electric charge via friction(Attempted) pith ball demonstration:

2 kinds of properties2 objects with same property repel each other2 objects with different properties attract each otherboth properties are always created together

Benjamin Franklin:kinds of charges are positive and negativeby convention, negative charge associated with amber

Conservation of Charge: The algebraic sum of all the electric charges in any closed system is constant.

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Conductors and Insulators

(Objects are usually “charged” by moving electric charge around, rather than creating or destroying charge.)

Conductor:

charge passes easily through the material

=> conductors contain charges which are free to move

Insulator:

charge cannot move (easily) through material

Semiconductor:

transition between insulator and conductor, usually of interest because of exotic electrical properties

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Charging by induction.

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Quantization and Conservation of Charge

Microscopic structure of matter: Atoms

Nucleus

most of mass

positive charge

composed of protons (each has charge = +e) and neutrons (no electric charge)

“orbitting” electrons (each has charge = e)

Atoms tend to be charge neutral

charge quantized: e = 1.6x10-19 C

Charge transfer usually in the form of addition or removal of electrons.

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Coulomb’s Law

A description of the interaction between two (point) charges

The magnitude of the Force exerted by one charge on the other

is proportional to the magnitude of each of the charges

is inversely proportional to the square of the distance between the charges

acts along a line connecting the charges

F kQq

r 2 k 1

4 0

8.988109 N m2

C2 9109 N m2

C2

Unit of charge is the Coulomb, a new type of quantity.

How big is 1 coulomb?

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Another form of Coulomb’s Law

the force exerted by Q (“source charge”) on q (“test charge”)

q toQ from

distance,

q toQ from

r,unit vectoˆ

qon Force

ˆ2

r

r

F

rrQq

kF

ˆ r

F

Q

q

r

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rrQq

kF ˆ2

ˆ r

F

Q

q

r

Coulomb’s Law: the force exerted by Q on q

Electric Charge and Electric Field (cont’d)

i i

i

i rr

qQk

rr

qQkr

r

qQk

FFF

ˆ

ˆˆ

2

222

212

1

1

21

r2

1F

Q1

q

r1

ˆ r 1

2F

Q2ˆ r 2

F

For several Sources

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•Analyze geometry/draw diagram

•calculate magnitude of each contribution

•calculate components of each contribution

•add contributions as vectors (add component by component)

Fi kQiq

ri2

A charge q = 5.0 nC is at the origin. A charge Q1 = 2.0 nC is located 2cm to the right on the x axis and and Q2 = 3.0 nC is located 4 cm to the right on the x axis. What is the net force on q?

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.3m

.3m

.4m

Q1 = 2.0 µC

Q2 = 2.0 µC

q = 4.0 µC

Geometry

Magnitudes

Components

Net Force

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Example: Compare the electric repulsion of two electrons to theirgravitational attraction

F kQq

r 2 k 9109 N m2

C2 F GMm

r 2 G 6.6710 11 Nm2

kg2

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Electric Field and Electric forcesElectric field is a “disturbance” in space resulting from the presence of (source) charge, which exerts a force on a (test) charge.

ˆ r

F

Q

q

r

ˆ r Q

P

r

ˆ r

qPF

PE

/)at (

)at (

Q

q

r )at (

) o(

qEq

qnF

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2

2

P toQ from

distance,

P toQ from

r,unit vectoˆ

Pat Field

ˆ

r

QkE

r

r

E

rrQ

kE

ˆ r Q

P

r

E

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r2

Q1r1

ˆ r 1

Q2ˆ r 2

For several Sources

i i

i

i rr

Qk

rr

Qkr

r

Qk

EEE

ˆ

ˆˆ

2

222

212

1

1

21

E

Force Law: F = qE

1E2E

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Elementary Electric Field Examples:•What is the electric field 30 cm from a +4nC charge?

•When a 100 volt battery is connected across two parallel conducting plates 1 cm apart, the resulting charge configuration produces a nearly uniform electric field of magnitude E = 1.00 E4 N/C.

Compare the electric force on an electron in this field with its weight.

What is the acceleration of the electron?

The electron is released from rest at the top plate.

What is the final speed of the electron as it hits the second plate?

How long does it take the electron to travel this distance?

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Electric Field Calculations

•Analyze geometry/draw diagram

Electric Field Contributions are directed away from positive charges, toward negative charges

•calculate magnitude of each contribution

•calculate components of each contribution

•add contributions as vectors (add component by component)

Ei kQi

ri2

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a

x

+Q

Q

Geometry

Magnitudes

Components

Net Force

a

Electric Dipole: two equal size(Q), opposite sign charges separated by a distance (l = 2a).

Determine the electric field on the x-axis

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a

x

+Q

Q

a

Ex 0

Ey k2aQ

x 2 a2 3 2

kp

x 2 a2 3 2

xa k

p

x 3

Field of an electric dipole

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a

x

Geometry

Magnitudes

Components

a

Line of charge: uniform line of charge (charge Q, l = 2a oriented along y-axis).Determine the electric field on the x-axis

y

dQ=dy

2222

222

22

cos

cossin

22

yx

xyx

dyk

EddE

yxdy

krdQ

kEd

yxr

rx

ry

aQ

ady

QdQ

x

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Add Components

Ex dEx

all charge

kdy

x 2 y 2 3 2

y a

ya

2ka

x x 2 a2

kQ

x x 2 a2

Ex kQ

x 2, x a

Ex k2k

x, x a

infinite line of charge: Er k2k

r

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Next: infinite sheet of charge is composed of of a series of infinite lines of charges

Look carefully at related textbook examples of a ring of charge, and a disk of charge.

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sheet of charge composed of a series of infinite lines of charge = charge per area

Electric Field due to an infinite sheet of charge

z

y

Geometry

Magnitudes

Components

2222

22

22

2

cos

22

cossin

yz

y

yz

dzkk

EddE

yz

dzkk

rk

Ed

yzr

ry

rz

dz

y

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Add Components

Ey dEy

all charge

2kydz

z 2 y 2z

z

2ky1

yarctan

z

y z

2k 2 2

2k

2 0

k 1

4 0

uniform electric field!!

z

y

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Interaction of an electric dipole with an electric field

dipole in a uniform electric field

x

y

zq

q

l

F=qE

F=qE

Ep

pE

lqE

Fl

Fl

RHRFr

F

z

iii

i

sin

sin

sin2

sin2

dipole ofcenter about torque

0

p

F = F = qE

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Work done rotating dipole in an electric field

watch directions of , an d

x

y

z

l

Ep

pEU

UpEpE

dpEW

dpEddW

cos)(

coscos

sin

sin

12

2

1p

d

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“Lines of Force”

Electric Field Lines: a means of visualizing the electric field=A line in space always tangent to the electric field at each point in space

concentration give indication of field strength

direction give direction of electric field

•start on positive charges, end on negative charges

•electric field lines never cross

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+ + + + + + + + + + + + + +