Chapter 2 hw quiz

What is the electric field at the center of a circle of radius R if the top half of the circle has a uniform charge +Q spread over the perimeter and the bottom half has a negative charge, -Q, uniformly spread over the perimeter?

+Q

-Q

One-dimensional problem:

dxxFWx

x

)(2

1

dx

dUxF )(

dxdx

dUx

x

2

1

)]()([ 12 xUxU

P218 Review: Conservative forces

Two-dimensional problem:

dyFdxFrdFWr

r

y

r

r

x

r

r 2

1

2

1

2

1

)]()([ 12 rUrU

y

UF

x

UF yx

;

veconservatiW does NOT depend on path!

veconservatiW around the closed path is zero!

Chapter 3. Electric Potential

• Constant electric field

• The Electric Potential: V

- Single Charge

- Dipole

EqF

- conservative? potential energy function?

€

rE d

r r

r r 1

r r 2

∫ = − limq0 → 0

1

q0

[U(r r 2) −U(

r r 1)] = −[V (

r r 2) −V (

r r 1)]

ExxVConstE )(

For a point charge at the origin:

r

qrV

04

1)(

Have a great day!

Please don’t forget your pictures

Hw: All Chapter 3 problems and exercisesReading: Chapter 3