Electic potential on a cone

[SummerPhysStudent]

Thanks for taking the time to look at this. I'm getting ready to go to grad school, and I'm realizing that although I did ok in my classes, there are large gaps in my knowledge of physics. That said, I'm currently trying to work my way through an E&M book, and now I'm stuck.

Here's the problem

Pretend that you have an open ended cone with the vertex at the origin and the fat end a distance located at a height R. Coincidently, the Radius of the cone at this height is also R. This cone also carries a uniform surface charge sigma. Find the potential difference between the vertex of the cone and the point at the center of the its base.

So obviously, V = 1 / (4 * pi * e0) * 2pi * int(sqrt(2)*r'dr / r) * sigma

(right)

so it's pretty easy to solve for the vertex, but I can't figure out how to solve the integral for the other point.
Thanks for the help
James

[maverick280857]

Try setting up the integrand using cylindrical coordinates (r, \theta, z) since that is an obvious choice for cylindrical symmetry (note: you can also use spherical coordinates...they might seem more logical at first sight).