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Two Coaxial Cylindrical Conducting Spheres
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Two long cylindrical conducting shells of radii a and b> a are arranged coaxi- ally and are charged to potentials 0, and Op respectively. Solve this problem by using the solutions to Laplace's equation for the potential o(ö), not with Gauss's Law. (It will help to think about the kind of symmetry you have before plunging into far too much algebra!) a) Find the electrostatic potential (7) inside the inner shell (i.e at radii r <a). b) Find the electrostatic potential o(r) in the region between the shells. c) Find the electrostatic potential o(r) everywhere outside the larger-radius shell (i.e at radii r >b). You will find it impossible to eliminate one of the arbitrary constants in the solution because of the logarithm. d) Give a clear explanation of the difficulty that led to the arbitrary constant remaining in your solution. Does this difficulty have physical consequences? If so, explain what these are. If not, discuss why not.