Please show all work and explain process. The first part of the problem and corr

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Please show all work and explain process. The first part of the problem and correct answer is in this link...

http://www.chegg.com/homework-help/questions-and-answers/electrostatics-work-explain-thought-process-q4838348

Consider any function V(s, phi, z) in the normal space, and use this mapping to define a function V( , , ) in the tilde space. (That is. if the above mapping takes a point in the normal space to a corresponding point in the tilde space.) Suppose further that V is independent of z. Show that its Laplacian in the normal and tilde spaceare related by 2V(s, phi, z) = C2s2(C - 1)/R2(C - 1) V( ). (Here 2 is the ordinary Laplacian but computed in tilde cylindrical coordinates.) Show that if V(s, phi, z) is a solution to the Poisson equation with some charge distribution rho(s, phi, z) and is independent of z in the normal space, then the corresponding potential in the tilde space is also a solution to Poisson's equation, but with some other charge distribution ( , phi, ) that is related by = f(s)rho(s, phi, z), where f(s) is some function. (What is this?) If the "normal space" is the problem in part. (a), then what is thecorresponding charge distribution in the tilde space? Find the value of C for which this mapping takes the boundary conditions of part (a) and maps them to the boundary conditions for general alpha. Using this mapping, find the electric potential V( ) that solves the boundary conditions and has the correct source.

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