Unit 5, Slide 1

Physics 2112Unit 5: Electric Potential Energy

Today’s Concept:Electric Potential Energy

Unit 5, Slide 2

Where we’re headed….

Force Energy2111

E Field

2112

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F

dr W = 0 Constant speed ( DK = 0 )

Fdr W > 0 Object speeds up ( DK > 0 )

W < 0 Object slows down ( DK < 0 )Fdr

Fdr

or

2

1

r

r

rdFW

KWTOT

Recall from Mechanics:

Unit 5, Slide 3

Unit 5, Slide 4

Prelecture Question

Masses M1 and M2 are initially separated by a distance Ra. Mass M2 is now moved further away from mass M1 such that their final separation is Rb.

Which of the following statements best describes the work Wab done by the force of gravity on M2 as it moves from Ra to Rb?

A. Wab > 0

B. Wab = 0

C. Wab < 0

Potential Energy

If gravity does negative work, potential energy increases!

Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases.

F

Dx Coulomb force does negative workPotential energy increases

veconservatiWU

+

+

+

+

Unit 5, Slide 5

A charge is released from rest in a region of electric field. The charge will start to move

A) In a direction that makes its potential energy increase.

B) In a direction that makes its potential energy decrease.

C) Along a path of constant potential energy.

F

Dx

It will move in the same direction as F

Work done by force is positive

DU = -Work is negative

Nature wants things to move in such a way that PE decreases

CheckPoint: Motion of Point Charge Electric Field

Unit 5, Slide 6

Example: Two Point Charges

d

Calculate the change in potential energy for two point charges originally very far apart moved to a separation of “d”

(Charged particles with the same sign have an increase in potential energy when brought closer together.)

For point charges often choose r = infinity as “zero” potential energy.

d

qqkU 21

q1

drr

qqkU

d

212

21

q2

Unit 5, Slide 7

d

qqkU 21

Example 5.1 (Velocity after a long time)

d = 10cm

The two charges shown below are held in place and then released. What is their final velocity after they have

q1 q2

Unit 5, Slide 8

m1 = 5X10-10kgq1 = +6nC

m2 = 7X10-10kgq2 = +8nC

CheckPoint: EPE of Point ChargeA charge of +Q is fixed in space. A second charge of +q was first placed at a distance r1 away from +Q. Then it was moved along a straight line to a new position at a distance R away from its starting position. The final location of +q is at a distance r2 from +Q.

What is the change in the potential energy of charge +q during this process?

A. kQq/RB. kQqR/r1

2

C. kQqR/r22

D. kQq((1/r2)-(1/r1))E. kQq((1/r1)-(1/r2))

Unit 5, Slide 9

Potential Energy of Many Charges

Two charges are separated by a distance d.

What is the change in potential energy when a third charge q is brought from far away to a distance d from the original two charges?

d

(superposition)

d

qQ

d

qQU

1

4

1

4 0

2

0

1

Q1

Q2

d

d

q

Electricity & Magnetism Lecture 5, Slide 10

• Don’t “double count”• No sines and cosines

CheckPoint: EPE of a System of Point Charges 1

Two charges which are equal in magnitude, but opposite in sign, are placed at equal distances from point A as shown. If a third charge is added to the system and placed at point A, how does the electric potential energy of the charge collection change?

Unit 5, Slide 11

A. Potential energy increasesB. Potential energy decreasesC. Potential energy does not changeD. The answer depends on the sign of the third charge

CheckPoint: EPE of a System of Point Charges 2

Two point charges are separated by some distance as shown. The charge of the first is positive. The charge of the second is negative and its magnitude is twice as large as the first. Is it possible find a place to bring a third charge in from infinity without changing the total potential energy of the system?

A. YES, as long as the third charge is positiveB. YES, as long as the third charge is negativeC. YES, no matter what the sign of the third chargeD. NO

Unit 5, Slide 12

Summary

rFor a pair of charges:

For a collection of charges:

Sum up for all pairs

Just evaluate

(We usually choose U = 0 to be where the charges are far apart)

Q1 Q2r

qqkU 21

r

qqkU 21

Unit 5, Slide 13