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Electric Potential/Separation of Variables

A rectangular pipe, running parallel to the z -axis (from −∞ to ∞), has three grounded metal sides, at y = 0, y = a, and x = 0. The fourth side,
at x = b, is maintained at a potential V0 (a constant).

(a) What is the potential within the pipe?

(b) Use a plotting program like Maple to plot the solution to zeroth order, first order, fifth order, and 100th order.

Use separation of variables of soln took about 4 pages but I cannot get the graph yet

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Here is my solution, including graphs it is 10 pages long. However, I'm bit confused about ...

Solution Summary

The electric potential and separation of variables are determined.