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Can Integrate solve this problem as I have posed it?

I am trying to calculate the electric field potential above a charged, insulating, disc. The simple version has the potential evaluated along the y-axis if the disc lies in the x-z plane and centred at the origin. In polar coordinates the integral is trivial analytically. I have set the same problem up in M10.1 in Cartesian coordinates and Integrate yields the correct result, although it takes some time to do this.

My real interest is being able to determine the potential at any point above the disc surface. At this point Integrate really struggles and I end up having to abort the execution. I can get a numerical solution with NIntegrate but I believe that an analytic solution should also be possible.

I have attached my notebook and would be grateful for any hints as how to proceed.

Many thanks, David

POSTED BY: David Mackay
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