Electric Potential Energy

Recall, for point masses, the force of gravity and gravitational potential energy are:

g 2

GMmF

r

g

GMmE

rand

1 22

kq qF

r 1 2kq q

Er

For point charges, it would follow that:

and

Electric Potential Energy

However, how are electric fields and gravitational fields different?

Unlike charges attract

+q -q

Like charges repel

+q +q

Therefore, electric potential energy can be positive or negative:

1 2kq qE

r

Electric Potential Energy

How do you increase the electric potential energy for charges?

UNLIKE CHARGES

+q -q

LIKE CHARGES

+q +q

Increase the separation between the charges.

Decrease the separation between the charges.

LOW potential energyHIGH potential energy

HIGH potential energyLOW potential energy

Electric Potential Energy

Electric potential energy is defined as zero when two charges are an infinite distance apart

gE 0 as r

The change in potential energy is the work done by the electrostatic force when moving a point charge from infinity to a distance r from another point charge.

+q

In other words, our reference “point” is infinity.

r W E

Electric Potential Energy

Electric potential energy versus separation graph

1 2kq qE

r

E

r0

Unlike charges

Like charges E 0

E 0

Electric Potential

All charges have the potential to store energy in their electric field.

+q1

+q2There is no potential energy stored until another charge is placed in the field of the first charge.

Electric Potential

The electric potential is defined as the electric potential energy per unit charge.

2

EV

q

For point charges:

units: volt (V)

1 V = 1 J/C

1kqVr

Electric Potential

Potential difference is the difference in electric potential from one point to another.

+q1

A

B

Also referred to as “voltage”

B AV V V

Potential difference is path independent

Electric Potential

Electric potential can be positive or negative depending on the sign of the charge producing the potential.

A positive charge produces a positive potential.

1kqVr

A negative charge produces a negative potential.

Electric Potential

Case 1: q1 > 0 and q2 < 0

+q1

If a negative charge (-1 C) is placed at A and then moved to B, potential energy should increase.

B AV V V

A

B

AV 2V

BV 1V

1V 2V 1V-q2

E q V 1C 1V 1J

Electric Potential

Case 1: q1 > 0 and q2 > 0

+q1

If a positive charge (+1 C) is placed at A and then moved to B, potential energy should decrease.

B AV V V

A

B

AV 2V

BV 1V

1V 2V 1V

E q V 1C 1V 1J

+q2

Electric Potential

Case 1: q1 < 0 and q2 < 0

If a negative charge (-1 C) is placed at A and then moved to B, potential energy should decrease.

B AV V V

A

B

AV 2V

BV 1V

1V 2V 1V-q2

E q V 1C 1V 1J

-q1

Electric Potential

Case 1: q1 < 0 and q2 > 0

If a positive charge (+1 C) is placed at A and then moved to B, potential energy should increase.

A

B

AV 2V

BV 1V

E q V 1C 1V 1J

+q2

B AV V V 1V 2V

1V

-q1

Electric Potential

The potential difference is related to the electric field strength.

A B

V

d

Two points, A and B, are separated by d and have a potential difference of:

d

V d

or

B AV V V

Electric Potential

Recall, Ohm’s Law:

V IR

Here, “V” actually refers to potential difference.

Why is current proportional to voltage?

V+

-R

I

Electric Potential

Equipotential lines can be drawn around charges to indicate constant electric potential.

+q1

At every point on this line, the electric potential is the same.

At every point on this line, the electric potential is the same.

Example Problem

For a point charge of 5e C, determine the following:

a) electric field strength 5.0 cm away from the charge

b) electric potential 5.0 cm away from the charge

c) electric potential energy if a -2e C charge is placed 5.0 cm from the 5e C charge

d) the work required to move the -2e C charge from 5.0 cm away to 10. cm away from the 5e C charge

Answers:

a) 2.9x10-6 N/C b) 1.4x10-7 V c) 4.6x10-26 J d) 2.3x10-26 N/C

Example Problem

Summary

In general:

W E

2

kq

r

EV

q

kqV

r

For point charges:

1 22

kq qF

r 1 2kq q

Er

F

q

V

d