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My plan of attack for the problem was to determine the potential at the apex and center of the base, and then subtract the two, since finding the E field doesn't seem too appealing (although by the symmetry, I can determine the direction of the E field along a path through the axis).

What I did was come up with a vvf to parameterize the cone. Then I need to find a formula for r in dV = dq / (4pi ep r). Then I integrate dV over the cone. The integral for the apex is simple and comes out nicely, but the other one is not so simple. Can anyone suggest something to make this process easier on me?