If 13 stationary source charges are placed at the vertices of a 13-sided polygon (a triskaidecagon), what is the total electric field provided by them at the geometric center of the triskaidecagon?

I have a numeric/symbolic answer but I'd like to see someone solve it to see if our results are the same, especially since explaining my way would involve appeals to geometric ideas I can't convey in ascii.

Are the charges identical, or arbitrary?
Is the polygon a regular polygon?

I understand the thread.

Pete: in order, your questions answered:
Yes
Yes

Pete; your solution?

Thanks CANGAS.
It is indeed natural to assume that the answers are as you suggest, but since the question is posed by SouthStar I'd rather he clarified it.

Cangas is right. Yes to both. I'd like also to see if anyone has the same ideas I do on generalizing to an n-gon (n>2).

By symmetry, the field at the center must be zero.

Did you mean the total electrostatic potential?

Ah yep. You're right. I had an analytic way of doing it though and Mathematica came up with ~3^-15, which is a poor excuse for 0.

I'm having trouble with this one though. You have a spherical shell of charge, radius a and surface density sigma from which a SMALL circular piece of radius b << a is removed. What is the direction and magnitude of the field at the center of the hole in the shell (ignoring the removed circular piece).

I got a field of 2*pi*sigma. I'd like to see if anyone can replicate.

Too much work for me, I think.