ch25 electric potential

7/30/2019 Ch25 Electric Potential

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Chapter 25

Electric Potential


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Electrical Potential Energy

When a test charge is placed in an electric field, it

experiences a force

If the test charge is moved in the field by some

external agent, the work done by the field is the

negative of the work done by the external agent

is an infinitesimaldisplacement vector that is

oriented tangent to a path

through space

oqF E

ds

+

+ ++++


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Electric Potential Energy, cont

The work done by the electric field is

As this work is done by the field, the potentialenergy of the charge-field system is changed

by U

For a finite displacement of the charge from A

to B,B

B A oA

U U U q d E s

od q d F s E s


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Electric Potential

The potential

The potential is characteristic of the field only

The potential is independent of the value ofqo

The potential has a value at every point in anelectric field

The potential energy per unit charge, U/qo, isthe electric potential

The electric potential iso

UV

q


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Electric Potential, cont.

The potential is a scalar quantity

Since energy is a scalar

As a charged particle moves in an electricfield, it will experience a change in potential


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Electric Potential, final

We often take the value of the potential tobe zero at some convenient point in thefield

Electric potential is a scalar characteristicof an electric field, independent of anycharges that may be placed in the field


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Work and Electric Potential

Assume a charge moves in an electric field

without any change in its kinetic energy

The work performed on the charge isWa-b = U= Ub-Ua = qV


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Units

1 V = 1 J/C

V is a volt

It takes one joule of work to move a 1-coulomb

charge through a potential difference of 1 volt


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Electron-Volts

Another unit of energy that is commonly used in

atomic and nuclear physics is the electron-volt

One electron-voltis defined as the energy a

charge-field system gains or loses when a charge ofmagnitude e(an electron or a proton) is moved

through a potential difference of 1 volt

1 eV = 1.60 x 10-19 J


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Potential Difference in a

Uniform Field

The equations for electric potential can be

simplified if the electric field is uniform:

The negative sign indicates that the electric

potential at point Bis lower than at pointA

Electric field lines always point in the direction of

decreasing electric potential

B B

B A A AV V V d E d Ed

E s s


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Energy and the Direction of

Electric Field

When the electric field is

directed downward, point

Bis at a lower potential

than pointA

When a positive test

charge moves fromA to B,

the charge-field system

loses potential energy


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More About Directions

A system consisting of a positive charge and anelectric field loses electric potential energy when thecharge moves in the direction of the field An electric field does work on a positive charge when the

charge moves in the direction of the electric field

The charged particle gains kinetic energy equal tothe potential energy lost by the charge-field system Another example of Conservation of Energy

Ifqo is negative, then Uis positive


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Equipotentials

The name equipotential surface is given to any surface

consisting of a continuous distribution of points having the

same electric potential


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Charged Particle in a Uniform

Field, Example

A positive charge isreleased from rest andmoves in the direction of theelectric field

The change in potential isnegative

The change in potentialenergy is negative

The force and acceleration

are in the direction of thefield


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Potential and Point Charges

A positive point charge

produces a field

directed radially

outward The potential difference

between pointsA and B

will be

1 1B A e

B A

V V k qr r


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Potential and Point Charges,

cont.

The electric potential is independent of the

path between pointsA and B

It is customary to choose a reference

potential ofV= 0 at rA =

Then the potential at some point ris

e

qV k r


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Electric Potential with Multiple

Charges

The electric potential due to several pointcharges is the sum of the potentials due toeach individual charge

This is another example of the superpositionprinciple

The sum is the algebraic sum

V= 0 at r=

i

e i i

qV k

r


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Potential Energy of Multiple

Charges

Consider two chargedparticles

The potential energy of

the system is

1 2

12

e

q qU k

r


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More About Uof Multiple

Charges

If the two charges are the same sign, Uis

positive and work must be done to bring the

charges together

If the two charges have opposite signs, Uis

negative and work is done to keep the

charges apart


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Uwith Multiple Charges, final

If there are more thantwo charges, then findUfor each pair ofcharges and add them

For three charges:

The result is independentof the order of thecharges

1 3 2 31 2

12 13 23

e

q q q qq qU k

r r r


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VDue to a Charged Conductor,

cont.

Vis constant everywhere on the surface of acharged conductor in equilibrium V= 0 between any two points on the surface

The surface of any charged conductor inelectrostatic equilibrium is an equipotential surface

Because the electric field is zero inside theconductor, we conclude that the electric potentialis constant everywhere inside the conductorandequal to the value at the surface


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E Compared to V

The electric potential is a

function ofr

The electric field is a

function ofr2

The effect of a charge on

the space surrounding it:

The charge sets up a

vector electric field which

is related to the force The charge sets up a

scalar potential which is

related to the energy


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Cavity in a Conductor

Assume an irregularly

shaped cavity is inside

a conductor

Assume no charges areinside the cavity

The electric field inside

the conductor must be

zero


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Cavity in a Conductor, cont

The electric field inside does not depend on thecharge distribution on the outside surface of theconductor

A cavity surrounded by conducting walls is a field-free region as long as no charges are inside thecavity

ch25 electric potential

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