Two infinitely-long lines of charge run parallel to the z axis. One has positive unifonn charge per unit length, IvO, and goes through the x y plane at x=O, y=s/2. The other has negative unifonn charge per unit length, -A, and goes through x=O, y=-s/2. Nothing changes with the z coordinate; the state of affairs in any plane parallel to the x y plane is the same in the x y plane.

Question

Two infinitely-long lines of charge run parallel to the z axis. One has positive unifonn charge per unit length, IvO, and goes through the x y plane at x=O, y=s/2. The other has negative unifonn charge per unit length, -A, and goes through x=O, y=-s/2. Nothing changes with the z coordinate; the state of affairs in any plane parallel to the x y plane is the same in the x y plane.
a. Describe the vector, R+, going from the positive line ofcharge to a
generic point, (x,y), and the vector R_ from the negative line.
b.
Find the total electric field at the point (x,y) as a vector.
c.
Find the voltage, V=V(x,y).
d.
To begin looking for equipotentials, set the voltage equal to a constant
called V = ~ In(a). Simplify and exponentiate to remove InO.
4n
e.
Multiply through by any denominators, then move everything to the left side and simplify.
f.
Find the multiplier, "2yc' " that multiplies y, and "complete the square"
by adding 2ycY to both sides.
g. Write the equation of an equipotential in the fonn x2 + (y -y c)2 = R2 and
find the radius and center.
h. Find numerical values for the voltage, center and radius for a=30, 10,3, I, 1/3, 1110, and 1/30.
1. Using s=four squares, draw these circles on graph paper.
J. Draw four or five lines of force of the electric field.