E&m Help

bjtstarks

27th October 2009 - 02:53 PM

Ok, I'm doing an assignment for my E&M class. I am having a little problem understanding how to do the problem. So I will type out the problem, and then explain my thought process so far.

QUOTE

Imagine a long conducting cylindrical shell (ignore edge effects) of radius, a, is split by the y-z plane and the two halves are isolated. The two halves are held at constant potentials PHI_1 (+x region) and PHI_2 (-x region).

a) Find the potential PHI in terms of a (cylinder radius), RHO (cylindrical coordinate radius), PSI (cylindrical coordinate angle measured from the +x axis), PHI_1, and PHI_2.

b) Find the surface charge density (SIGMA) on each half of the cylinder.

So, my thoughts on this were to use conformal mapping to solve this problem. From what I can remember conformal mapping will be the easiest way to solve this problem, but I can't for the life of me remember how to do it even when I read my books.

If I am thinking correctly in this regard, please let me know and help me get the process started, or if not a hint in the right direction would be greatly appreciated.

rpenner

27th October 2009 - 07:14 PM

Maybe you need just a push.

http://math.fullerton.edu/mathews/c2003/El...staticsMod.html

To find phi(rho, psi) = phi(z = rho e^(i psi))

You might want to use the mapping

u + iv = w = ln((a-z)/(a+z)) = ln((a+rho e^(i psi))/(a-rho e^(i psi)))

for the interior of the disk.

aalpha.org

29th October 2009 - 07:35 AM

QUOTE (bjtstarks+Oct 27 2009, 02:53 PM)

Ok, I'm doing an assignment for my E&M class. I am having a little problem understanding how to do the problem. So I will type out the problem, and then explain my thought process so far.

So, my thoughts on this were to use conformal mapping to solve this problem. From what I can remember conformal mapping will be the easiest way to solve this problem, but I can't for the life of me remember how to do it even when I read my books.

If I am thinking correctly in this regard, please let me know and help me get the process started, or if not a hint in the right direction would be greatly appreciated.

we can do it for u,

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