Unit 5, Slide 1

Physics 2112

Unit 5: Electric Potential Energy

Today’s Concept:

Electric Potential Energy

Unit 5, Slide 2

Where we’re headed….

Force Energy2111

E Field

2112

???

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 D=

Recall from Mechanics:

Unit 5, Slide 3

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 D

+ +

+

Unit 5, Slide 4

WH is the work done by the hand on the ballWE is the work done by the electric field on the ball

Which of the following statements is true:

A) WH > 0 and WE > 0

B) WH > 0 and WE < 0

C) WH < 0 and WE < 0

D) WH < 0 and WE > 0

You hold a positively charged ball and walk due east in a region that contains an electric field directed due west.

Question

Unit 5, Slide 5

FE FH

drE

drE

FE FH

B) WH > 0 and WE < 0

Conservative force: DU = WENot a conservative force.Does not have any DU.

Is DU positive or negative?

A) Positive

B) Negative

Question

Unit 5, Slide 6

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=D

q1

drr

qqkU

d

2

12

21

=Dq2

Unit 5, Slide 7

d

qqkU 21=

Prelecture Question

In case A two opposite charges which are equal in magnitude are separated by a distance d. In case Bthe same charges are separated by a distance 2d. Which configuration has the highest potential energy?

A) Case A

B) Case B

Unit 5, Slide 8

d

2d

Case A

Case B

Clicker Question Discussion

Unit 5, Slide 9

U(r)

0

r

UA > UB

2

0

1

4 2B

qU

d=

U(2d)

2d

Case B

r

qqrU

1

4)(

0

21

=

dCase A

U(d)

r

qU A

1

4 0

2

=

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 moved a great distance apart?

q1q2

Unit 5, Slide 10

m1 = 5X10-10kg

q1 = +6nCm2 = 7X10-10kg

q2 = +8nC

Pause to connect to 2111

Unit 5, Slide 11

When we said

“The ball has mgh of potential energy.”

we really meant

“The ball-earth system has mgh of potential

energy.”

Why could we ignore earth?

Why can’t we ignore the other charges now?

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

+=D

Q1

Q2

d

d

q

Electricity & Magnetism Lecture 5, Slide 12

• Don’t “double count”

• No sines and cosines

What is the total work by the electric field when three identical charges by brought from infinitely far away to the points on an equilateral triangle.

A) 0

B)

C)

D)

E) d

dd

Work to bring in first charge: W1 = 0

Q

Q

Q

Work to bring in second charge :d

QW

2

0

24

1

=

Work to bring in third charge :d

Q

d

Q

d

QW

2

0

2

0

2

0

34

2

4

1

4

1

==

d

QW

1

4 0

2

=

d

QW

1

4 0

2

+=

d

QW

1

43

0

2

=

d

QW

1

43

0

2

+=

Potential Energy of Many Charges

Electricity & Magnetism Lecture 5, Slide 13

conWU =Dd

Qk

2

3+=

What is the total work by the outside force when it brings three identical charges from infinitely far away to the points on an equilateral triangle?

A) 0

B)

C)

D)

E) d

dd

Q

Q

Q

d

QW

1

4 0

2

=

d

QW

1

4 0

2

+=

d

QW

1

43

0

2

=

d

QW

1

43

0

2

+=

Potential Energy of Many Charges

Electricity & Magnetism Lecture 5, Slide 14

Now lets say the second charge is negative. Now what is the total work done by the field to bring the three charges in?

A) 0

B)

C)

D)

E) Q Q

Q

d

dd

Work to bring in first charge: W1 = 0

1

Work to bring in second charge :

2

Potential Energy of Many Charges

Unit 5, Slide 15

d

QWW i

2

04

1

+==

d

QU

2

04

1

=D

d

QW

1

41

0

2

+=

d

QW

1

41

0

2

=

d

QW

1

42

0

2

=

d

QW

1

42

0

2

+=

d

QW

2

0

24

1

+=

Work to bring in third charge : 04

1

4

1 2

0

2

0

3 =+=d

Q

d

QW

d

QkU

2

=D

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 16

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 17

Example 5.2

A positive charge q is placed at x = 0 and a negative charge 2q is placed at x = d.

At how many different places along the x axis could another positive charge be placed without changing the total potential energy of the system?

Unit 5, Slide 18

xX = 0 X = d

A) 0

B) 1

C) 2

D) 3

Q 2Q

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 Q2

r

qqkU 21=

r

qqkU 21=

Unit 5, Slide 19