Potential of two parallel infinite wires

[BenBa]

Homework Statement

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.

Homework 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.

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...

 

[Simon Bridge]

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...

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 $y=(x-d)^2$.