# Potential of two parallel infinite wires

1. Feb 13, 2014

### BenBa

1. The problem statement, all variables and given/known data
Two parallel infinite wires lay parallel to the z-axis in the xz-plane. One located at x=d has charge distribution λ and one located at x=-d has charge distribution -λ.

2. Relevant equations

a) Find the potential V(x,y,z) using the origin as a reference
b)Show that the equipotential surfaces are circular cylinders parallel to, but not coaxial with, the wires. For a given V_0 determine the corresponding axis and radius of the cylinder.

3. The attempt at a solution

I believe we can approach this problem with gaussian surfaces, but i am confused on how to exactly use the fact that the origin is a reference. Also the fact that its in cartesian is messing with my ability to do the problem, there is so much cylindrical symmetry...

2. Feb 13, 2014

### Simon Bridge

Normally you'd do this problem for one wire, with the wire along the x axis or similar.

This gives you an equation for the electric field about that axis.
What happens to that equation if the wire is not on the axis?

Hint: if a simple parabola were centered on the y axis it would have equation $y=x^2$, if it were now centered on the line x=d, it would have equation $y=(x-d)^2$.