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LECTURE 7 slide 1

Lecture 7

Electrostatic Potential

Sections: 4.1, 4.2, 4.3, 4.4

Homework: D4.1, D4.2, D4.3, D4.4, D4.5; 4.3, 4.4, 4.5, 4.6,

4.9, 4.10, 4.12

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LECTURE 7 slide 2

Work 1

differential work

cosW dW d FdL = = =F L F L

work done fromA toB

, JB

W d= F L

work is positive if the applied force is in thedirection of displacement

work is negative if the applied force is opposite to the direction

of displacement

FL

0W F L = >

F L

0W F L =

cos 0, rock gains energyg gW F L =

L

gF

mF

0m mW F L= F L E L BextF

E Q=F E

displacem

ent

Q

+ + + + +

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LECTURE 7 slide 8

Work of Electric Field to Move Charges

if charge is already atB and is free to move, the electric field will

bring it back toA at the expense of its own energy (charge loses

potential energy WE)

0

A B

E E

B A

W Q d W Q d = = = > E L E L

A B

B Ad d = E L E L

B

displa

cementE Q=F E

+ + + + +

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LECTURE 7 slide 9

Electrostatic Potential Difference (Voltage)

Definition 1:potential difference VAB is the work done by the electric field in

moving a unit test charge from pointA to pointB

, VB

AB

A

V d= E L

Definition 2:

potential difference VAB is the work done by external forces in

moving a unit test charge from pointB to pointA

, VA

AB

B

V d= E L

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LECTURE 7 slide 10

Example: Potential Difference in the Field of Line Charge

Find the voltage VABbetween pointA(A,A,zA) and pointB(B,B,zB)in the field of a line charge l along thezaxis. Take the path along

the line segments: 1) , ,2) , ,

3) , ,

A A B A

B A B

B B B

z zz z z

z z

= == =

= =

00

( , , ) ( , , )

( , , )

B B

A AB

A

zB

AB A A A A B z

A z

B B

V d z d z dz

z d

= = + +

E L E a E a

E a

1

2

l

= E a

ln2

l BAB

A

V

= Can we choose B orA at infinity

or at zero?

note independence of angular position

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LECTURE 7 slide 11

Electrostatic Potential

Definition 1:the potential at a pointA is the work done by the electric field in

moving a unit test charge from pointA to a reference pointA0where the potential is assumed equal to zero

0

0

, V

A A

A

A A

V d d= =

E L E L

Definition 2:

the potential at a pointA is the work done by an external force in

moving a unit test charge from a reference pointA0, where the

potential is assumed equal to zero, to the pointA.

the electrostatic potential is the potential energy of a unit test

charge

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LECTURE 7 slide 12

Potential of a Point/Spherical Charge

1

4 AA

QV

=

N24A

A R RA R d

QV d dR

R

= =

LE L a a

assume potential is zero at infinity

integrate along any radial line

1

4

A

A

QV

=

+ A

E

the potential is the same for all points on the sphere of radius RA

we say that the sphere is an equipotential surface

notice the 1/R dependence on distance and compare it with E

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LECTURE 7 slide 13

You have learned:

how to compute work integrals

what potential difference (voltage) is in field theory

what we mean by a positive and a negative work

what absolute potential is

that the potential of a point/spherical charge depends on distance

as 1/R unlike E which decreases as 1/R2

what the potential difference is in the field of a line charge