Potential distribution in metal cylinder

AI Thread Summary
The discussion focuses on modeling an electrode within a metal cylinder, specifically addressing the potential distribution described by boundary conditions at z=0 and z=H. The user is struggling with solving the Poisson equation, particularly with Bessel functions, and is seeking alternative methods. Participants suggest that the symmetry of the problem is crucial and that Bessel function expansion is a straightforward approach. They also note that solutions to similar problems are commonly found in mathematical physics and electromagnetism textbooks. Overall, the conversation emphasizes the importance of understanding boundary conditions and available mathematical resources for solving the problem.
vickcro
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I have an electrode that I'm trying to model. It's got v=0 at z=0, and v=V at z=H. I've been playing around with the poisson equation, and keep getting terrible solutions to PDEs involving Bessel functions. Anyone know if there's a better way to do this (since I can't seem to solve it with the boundary conditions anyhow...and it's not a homework problem, so there's no one to ask)

Thanks!
 
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What kind of symmetry is there?
 
The answer depends on the boundary condition at r=R.
Bessel function expansion is the easiest way to do it.
The solution is given in most math-physics and EM textbooks.
 

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