Can Green's Function Solve Poisson's Equation in Cylindrical Geometry?

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SUMMARY

The discussion centers on finding a general solution to Poisson's equation in cylindrical geometry, specifically between two concentric hollow cylinders of finite height. The user seeks to utilize Green's function to derive the field solution in this configuration. They have existing solutions for spherical and Cartesian geometries but require assistance with cylindrical geometry. The mention of polar coordinates suggests a potential avenue for exploration in this context.

PREREQUISITES
  • Understanding of Poisson's equation and its applications
  • Familiarity with Green's function methodology
  • Knowledge of cylindrical coordinate systems
  • Basic concepts of electrostatics and field theory
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  • Research the application of Green's function in cylindrical coordinates
  • Study the derivation of solutions for Poisson's equation in cylindrical geometries
  • Explore the implications of boundary conditions in cylindrical systems
  • Investigate the transition from cylindrical to polar coordinates in solving differential equations
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Physicists, mathematicians, and engineers focusing on electrostatics, field theory, and differential equations in cylindrical geometries.

pfknapp
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Hey everyone,
first time poster. I am looking for a general solution to poisson's equation in a cylindrical geometry. By general, I am thinking of two concentric hollow cylinders of finite height, and the solution for the field using the green's function in between the two cylinders. With this kind of geometry one can take the limit as either the inner radius goes to zero or the outer radius goes to infinity and therby cover all your bases and have the solution everywhere. Let me know if you can help. I have general solutions for spherical and cartesian, but I can't seem to find one for cylindrical. Thanks everyone.
 
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What about polar coordinates?
 

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