What makes a square equipotential?
Channel: James Rantschler
Date: 04/10/2013

I'll give you an electrostatic potential with square equipotentials, and you're to find (a) the associated electric field and (b) the charge distribution that creates it.

The potential is:

V(x,y,z) = V'_0 * max(|x|,|y|)

V'_0 is just a constant with dimensions of [V]/[x].  max(a,b) is the maximum of a and b.  Draw one or two equipotentials out, and you'll see what it looks like.

Hint: translate the maximum into a piecewise form, and don't forget to use some of the rules I gave you for dealing with discontinuities when taking the divergence.