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Announcements. Homework for tomorrow… (Ch . 28 CQ1, Probs. 7 & 37) 26.50: a) 3.6 x 10 3 N/Cb) Δ y = 9.6 x 10 3 m 27.26: E 1 = 0 N/C, E 2 = 0 N/ C, E 3 = 8.0 x 10 -9 N /C 27.27: a) (2.5 x 10 4 N/ C) jhat b) 0 N/ Cc) -( 2.5 x 10 4 N/C) jhat Office hours…

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Announcements

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### Announcements

• Homework for tomorrow…

(Ch. 28 CQ1, Probs. 7 & 37)

26.50: a) 3.6 x 103 N/Cb) Δy = 9.6 x 103 m

27.26: E1 = 0 N/C, E2= 0 N/C, E3= 8.0 x 10-9 N/C

27.27: a) (2.5 x 104N/C) jhat b) 0 N/Cc) -(2.5 x 104 N/C) jhat

• Office hours…

MW 12:30-1:30 pm

TR 9-10 am

F 10-11 am

• Tutorial Learning Center (TLC) hours:

M 8-1 pm, 3-6 pm,W 8-1 pm, 2-6 pm

TR 8-6 pm, F 8-2 pm

## Chapter 28

The Electric Potential

(Potential Energy of Point Charges)

### Last time…

Work done by a constant, variable force…

Potential energy defined…

Potential energy of a charge q in a uniform E-field…

### Quiz Question 1

Two negative charges are equal.

Which has more electric potential energy?

• Charge A.

• Charge B.

• They have the same potential energy.

• Both have zero potential energy.

### Quiz Question 2

A positive point charge is moved from i to f in the non-uniform E-field shown. During this process…

• E decreases, ΔU increases, W by the field is negative.

• E increases, ΔU increases, W by the field is negative.

• E decreases, ΔU decreases, W by the field is negative.

• E decreases, ΔU decreases, W by the field is positive.

• E is constant, ΔU decreases, W by the field is positive.

i

f

### 28.2:The Potential Energy of Point Charges

Calculate the…

• work done by the E-field of q1on q2

• the change in potential energy of the system as q2 moves from xi to xf.

### The Potential Energy of Point Charges

The electric potential energy between two point charges is…

Notice:

• This is the potential energy of the system of charges.

• We’ve chosen the zero point of U at r ->∞.

• Potential energy of two like charges is positive and of two opposite charges is negative.

• Also holds for uniform sphere of charge.

### Mechanical Energy Conservation…

• The total energy, Emech , is a horizontal line because mechanical energy is conserved.

• When Emech> 0, unbounded system.

• Emech= Uelec at r = rmin, where K = 0.

• rminis the distance of closest approach (a turning point).

### Mechanical Energy Conservation…

• The total energy, Emech , is a horizontal line because mechanical energy is conserved.

• When Emech< 0, bound system.

• Emech= Uelec at r = rmax, where K = 0.

• rmaxis the maximum separation distance (a turning point).

### Quiz Question 3

A positive and a negative charge are released from rest in vacuum. They move toward each other. As they do:

• A positive potential energy becomes more positive.

• A positive potential energy becomes less positive.

• A negative potential energy becomes more negative.

• A negative potential energy becomes less negative.

• A positive potential energy becomes a negative potential energy.

### i.e. 28.3: Escape velocity

An interaction between two elementary particles causes an electron and a positron (a positive electron) to be shot out back to back with equal speeds.

What minimum speed must each have when they are 100 fm apart in order to escape each other?

### Multiple Point Charges

What is the electric potential energy of 3 pt charges?

q1

r12

r13

q2

r23

q3