[SOLVED] Physics 311 Homework Set 4

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 2.34. 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 2.66. 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, (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 dierent ways.)