chapter 2 hw quiz what is the electric field at the center of a circle of radius r if the top half...
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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