Description
1. Consider four point charges located at the corners of a square with charges and coordinates
q1 = q @ x = y = 0 , q2 = 2q @ x = ` , y = 0
q3 = q @ x = y = ` , q4 = 3q @ x = 0 , y = `
(1) a) Draw a diagram showing the position of each of the charges.
b) On the diagram, show the the direction of the force acting on q1 due to q2; due to q3;
due to q4.
c) Calculate the the net force on q1 due to the other charges in unit-vector notation.
2. a) Find the net charge on a solid sphere of radius R with a volume charge density
⇢(✓) = ⇢0 cos2 ✓. (2)
b) Find the net charge on a circular plate of radius R with a surface charge density
(s) = 0
R
s . (3)
3. Problem 2.3
4. Find the electric field a distance z above one end of a straight line segment of length L,
which carries a non-uniform line charge density
(x) = 0
x2
L2 . (4)
5. Problem 2.6
6. Find the electric field a distance z above the center of a flat circular disk of radius R,
which carries a non-uniform surface charge density
(s) = 0
s
R (5)
7. Suppose the electric field in some region is found to be
E~ = kr5
r, ˆ (6)
in spherical-polar coordinates, where k is a constant.
a) Find the charge density ⇢.
b) Find the total charge contained in a sphere of radius R, centered at the origin. (Do it
two di↵erent ways.)