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Chapter 19

Elec tr ic Po ten t ial Energyand the

Elec tr ic Potent ial


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Electric potential energy and the

electric potential

Potential energy

The electric potential difference Equipotential surfaces and their relation to

electric field

Capacitors and dielectric


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19.1Potential Energy

BABAAB mghmghW GPEGPE

Gravitational exerts a force, F=mg on the basketball of mass m. work is done by

the gravitational force as the ball falls from A to B.


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Because of the electric field E, an electric force, F=qoE is exerted on a positive

test charge, +qo. Work is done by the force as the charge moves from A to B


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BAABW EPEEPE

Work done by electric force equal the

difference between the electric potential

energy, EPE at A and the electricpotential energy at B.


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19.2The Electr icPotential Differenc e

BA

o

AB

o

B

o

A

o

AB

VVq

W

qqq

W

EPEEPE

The potential energy per unit charge

is called the electric potential, V.


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DEFINITION OF ELECTRIC POTENTIAL

The electric potential at a given point is the electric potential energy

of a small test charge divided by the charge itself:

oqV

EPE

SI Unit of Electr ic Potential :joule/coulomb = volt (V)

o

AB

o

A

o

BAB

q

W

qqVV

EPEEPE

o

AB

o q

W

qV

EPE


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Examp le 1Work, Potential Energy, and

Electric Potential

The work done by the electric force as the

test charge (+2.0x10-6C) moves from A to

B is +5.0x10-5J.

(a) Find the difference in EPE between these

points.

(b) Determine the potential difference between

these points.

BAABW EPEEPE

o

AB

o

A

o

BAB

q

W

qqVV

EPEEPE


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BAABW EPEEPE (a)

J100.5EPEEPE 5 ABAB W

(b)

V25

C102.0

J100.56-

5

o

ABAB

q

WVV


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Conceptual Examp le 2The Accelerations of Positive and Negative Charges

A positive test charge is released from A and accelerates towards B. Upon

reaching B, the test charge continues to accelerate toward C. Assuming that

only motion along the line is possible, what will a negative test charge do when

released from rest at B?

A positive charge accelerates from a region of higher electric potential

toward a region of lower electric potential.

A negative charge accelerates from a region of lower potential toward

a region of higher potential.


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We now include electric potential energy EPE as part of the total

energy that an object can have:

EPEkxmghImvE 2212

212

21

One electron vol t is the magni tud e of the amo unt b y wh ich the potent ia l

energy of an electron changes when the electron mo ves throug h a potent ial

di f ference of o ne vol t .

V1060.1eV1 19


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Examp le 4The Conservation of Energy

A particle has a mass of 1.8x10-5kg and a charge of +3.0x10-5C. It is released from

point A and accelerates horizontally until it reaches point B. The only force actingon the particle is the electric force, and the electric potential at A is 25V greater than

at B. (a) What is the speed of the particle at point B? (b) If the same particle had a

negative charge and were released from point B, what would be its speed at A?


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AABB EPEmvEPEmv 2

212

21

BAAB EPEEPEmvmv 2

212

21

BAoAB VVqmvmv 221221

f f


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BAoB VVqmv 2

21(a)

sm1.9kg108.1V25C100.32

2

55

mVVqv BAoB

sm1.9kg108.1V25C100.32

2

55

mVVqv BAoA(a)

19 3 Th El t i P t t i l Dif f C t d b P i t Ch


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19.3The Electr ic Potential Difference Created by Po int Charges

BAo

ABAB

r

kq

r

kq

q

WVV

Potential of a

point charger

kqV



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Examp le 5The Potential of a Point Charge

Using a zero reference potential at infinity,

determine the amount by which a point chargeof 4.0x10-8C alters the electric potential at a

spot 1.2m away when the charge is

(a) positive and (b) negative.



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V300

m2.1

C100.4CmN1099.88229

rkqV

(a) Positive charge

(b) Negative charge

V300V


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A single point charge raises or lowers the

potential at given location, depending on

whether the charge is positive or negative

When or more charges are present, the

potential due to all charges is obtained by

adding together the individual potentials

19 3 The Electr ic Potential Dif ference Created by Po int Charges


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Examp le 6The Total Electric Potential

At locations A and B, find the total electric potential.

19 3 The Electr ic Potential Dif ference Created by Po int Charges


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V240m60.0

C100.8CmN1099.8

m20.0

C100.8CmN1099.8 82298229

AV

V0m40.0

C100.8CmN1099.8

m40.0

C100.8CmN1099.8 82298229

BV

19 4 Equip otential Surfaces and Their Relat ion to th e Electr ic Field


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19.4Equip otential Surfaces and Their Relat ion to th e Electr ic Field

An equipo tent ial surface is a surface on

which the electric potential is the same everywhere.

r

kqV

The net electric force does no work on a charge as

it moves on an equipotential surface.



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The electric field created by any charge

or group of charges is everywhere

perpendicular to the associated

equipotential surfaces and points in

the direction of decreasing potential.



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s

VE



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Examp le 9The Electric Field and Potential

Are Related

The plates of the capacitor are separated by

a distance of 0.032 m, and the potential difference

between them is VB-VA=-64V. Between the

two equipotential surfaces shown in color, there

is a potential difference of -3.0V. Find the spacingbetween the two colored surfaces.



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mV100.2m0.032

V64 3

s

VE

m105.1mV100.2

V0.3 33

E

Vs

19 5 Capacitors and Dielectr ic s


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19.5Capacitors and Dielectr ic s

A parallel plate capacitor consists of two

metal plates, one carrying charge +q and

the other carrying charge q.

It is common to fill the region between

the plates with an electrically insulating

substance called a dielectr ic.

19.5 Capacitors and Dielectr ic s


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THE RELATION BETWEEN CHARGE AND POTENTIAL

DIFFERENCE FOR A CAPACITOR

The magnitude of the charge in each place of the

capacitor is directly proportional to the magnitude

of the potential difference between the plates.

CVq The capacitance Cis the proportionality constant.

SI Unit o f Capacitance:coulomb/volt = farad (F)

19.5 Capacitors and Dielectr ic s


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THE DIELECTRIC CONSTANT

If a dielectric is inserted between the plates of

a capacitor, the capacitance can increase markedly.

Dielectr ic con stant

E

Eo



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p



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p

THE CAPACITANCE OF A PARALLEL PLATE CAPACITOR

d

VEE o

AqE oo

Vd

Aq o

d

AC o

Paral lel plate capacito r

f i l led with a dielectr ic



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p

Conceptual Examp le 11The Effect of a Dielectric When a

Capacitor Has a Constant Charge

An empty capacitor is connected to a battery and charged up.

The capacitor is then disconnected from the battery, and a slab

of dielectric material is inserted between the plates. Does the

voltage across the plates increase, remain the same, or

decrease?



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p

Examp le 12A Computer Keyboard

One common kind of computer keyboard is based on theidea of capacitance. Each key is mounted on one end

of a plunger, the other end being attached to a movable

metal plate. The movable plate and the fixed plate

form a capacitor. When the key is pressed, the

capacitance increases. The change in capacitance is

detected, thereby recognizing the key which hasbeen pressed.

The separation between the plates is 5.00 mm, but is

reduced to 0.150 mm when a key is pressed. The

plate area is 9.50x10-5m2 and the capacitor is filled with

a material whose dielectric constant is 3.50.

Determine the change in capacitance detected by the

computer.



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F106.19

m100.150

m1050.9mNC1085.850.3 123-

252212

d

AC o

F10589.0

m105.00

m1050.9mNC1085.850.3 123-

252212

d

AC o

F100.19 12C



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ENERGY STORAGE IN A CAPACITOR

221Energy CV

2

2

1

Energy Edd

Ao

2

21

Volume

EnergydensityEnergy Eo

AdVolume

19.6Biom edical App l icat ions of Electr ica l Potent ia l Di f ferences


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