Potential distribution in metal cylinder

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SUMMARY

The discussion focuses on modeling an electrode within a metal cylinder using the Poisson equation, specifically addressing boundary conditions where the potential is zero at z=0 and V at z=H. The participants suggest that Bessel function expansion is the most effective method for solving the associated partial differential equations (PDEs). They emphasize that the solution can be found in standard mathematical physics and electromagnetism textbooks, indicating a well-established approach to the problem.

PREREQUISITES
  • Understanding of Poisson's equation in electrostatics
  • Familiarity with Bessel functions and their applications
  • Knowledge of boundary value problems in partial differential equations
  • Basic concepts of cylindrical symmetry in electromagnetism
NEXT STEPS
  • Study Bessel function properties and their role in solving PDEs
  • Review mathematical physics textbooks for solutions to similar boundary value problems
  • Explore numerical methods for solving Poisson's equation in cylindrical coordinates
  • Investigate advanced topics in electrostatics related to cylindrical geometries
USEFUL FOR

Researchers, physicists, and engineers working on electrostatics, particularly those involved in modeling electrode behavior in cylindrical geometries.

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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