Actual electrostatics question

[§outh§tar]

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.

[Pete]

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

[CANGAS]

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?

[Pete]

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.

[§outh§tar]

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).

[Pete]

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

Did you mean the total electrostatic potential?

[§outh§tar]

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.

[Pete]

Too much work for me, I think.