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1

PHYS 1022: Chap. 29, Pg 2 New Topic

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PHYS 1022: Chap. 29, Pg 3

Topics: •  Electric Potential Energy •  The Potential Energy of Point Charges •  The Potential Energy of a Dipole

PHYS 1022: Chap. 29, Pg 4

  Define potential energy function U via the work done by a conservative force F in the following way:

The work done by a conservative force is equal to the decrease in the potential energy function.

  Conservative force   Work done by a conservative force does not depend on the path. It only

depends on the initial and final positions.

Click here for P.E.

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PHYS 1022: Chap. 29, Pg 5

Gravity Electric

PHYS 1022: Chap. 29, Pg 6

A negative charge is moved from a to b in a uniform electric field as shown. What happens to the potential energy of the charge?

1)  increase 2)  decrease 3)  stays the same

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PHYS 1022: Chap. 29, Pg 7

+ + + + + +

- - - - - -

+

-

+ + + + + +

- - - - - -

PHYS 1022: Chap. 29, Pg 8

5

PHYS 1022: Chap. 29, Pg 9

PHYS 1022: Chap. 29, Pg 10

  It depends on the sign of the charges.

Relative to what point is this potential energy defined?

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PHYS 1022: Chap. 29, Pg 11

For a pair of charges

For a system of 3 charges

Generalization to N charges

Avoid double-counting. Watch for sign of charges.

q1

q3

q2

r13

r12

r23

Physical meaning of U: the total work done by us to assemble the charges from infinity to the present configuration.

PHYS 1022: Chap. 29, Pg 12

Which group of charges took more work to bring together from a very large distance

apart ?

+1 +2 d

+1

+1

+1

d d

d

1)  Case a 2)  Case b 3)  Both the same

7

PHYS 1022: Chap. 29, Pg 13

PHYS 1022: Chap. 29, Pg 14

+

- -

2 nC

-1 nC -1 nC

3 cm

3 cm

3 cm

8

PHYS 1022: Chap. 29, Pg 15

Initially the inner shell has a net charge +q, and the outer shell has no net charge. How much work must be done to add –q of charge to the outer shell?

+q

PHYS 1022: Chap. 29, Pg 16

The potential energy of an electric dipole p in a uniform electric field E is

The potential energy is minimum at φ = 0° where the dipole is

aligned with the electric field.

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PHYS 1022: Chap. 29, Pg 17

  Rank in order, from most positive to most negative, the potential energies U1 to U6 of these six electric dipoles in a uniform electric field.

PHYS 1022: Chap. 29, Pg 18 New Topic

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PHYS 1022: Chap. 29, Pg 19

  Definition: potential is defined as potential energy per unit charge:   SI unit: volt. 1 V = 1 J/C

For example: the potential energy between two point charges

q q0 r

Therefore, the potential of point charge q is

For a system of point charges:

Potential is a scalar. There’s no direction to worry about. But you do have to watch the sign of the charges.

(algebraic sum)

PHYS 1022: Chap. 29, Pg 20

. P

r

Q

Relative to which point is this potential defined? infinity

11

PHYS 1022: Chap. 29, Pg 21

+ + + +

1 mm

3 mm