Chapter 3

Question 1

Method of Images

Set Up

A charge at x0 and a plate along yz plane

Find F on q

Answer 1

X <0
V(x<0,y,z) =0
X>=0
V(xyz)= 1/4pie(q/(x-x0^2 +y^2+z^2)-q/(x+x0^2 +y^2+z^2)

F= k q1qi/(r^2)
Force of imaginary on real q
F= 1/4pie(q^2/2x0)^2

Question 2

Method of Images

Set Up

A charge at x0 and a plate along yz plane

Find W on q

Answer 2

W=-1/4pie q^2/2x0
W= e/2 int(E^2)dV

Question 3

Method of Images

Set Up

A charge at a0 and a conducting sphere with radius R

Find potential outside the sphere

Question 4

Grounded conductor/ infite conductor

Answer 4

V=0

Question 5

Conductor

Answer 5

V=const

Question 6

Charge density

Answer 6

Sigma = -e dv/dn

Question 7

Induced charge

Answer 7

Q=INT(sigma )DA

Question 8

2 parallel charges one conductor perpendicular to the charge

What are the forces on charge 1

Answer 8

Force of 2 on 1 f= - (1/ 4pie)(q1q2/r^2)
Force of imaginary 2 on 1
Force of imaginary 1 on 1
Two are not real forces but forces from the conductor

Question 9

E field of a conducting spher

Answer 9

Inside 0
Outside
E = Q/ 4pie r^2
The same as a point charge

Question 10

E field of a conducting sphere with a hole r

Question 11

What is the Laplace equation

Answer 11

A form of poisons equation
◇^2V(xyz) =-p(xyz)/e
Solution
◇^2V=0

Question 12

Steps of separation of varriables

Answer 12

1. Laplace
2. Separate
3. Boundaries that go to Infinity
4. the rest

Question 13

Ode d^2X/dx^2 = v^2x

Answer 13

X = Ae^vx + Be^-vx

Question 14

Ode d^2X/dx^2 = -v^2x

Answer 14

X= Asin(vx) +Bcos(vx)