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2) Assume you have an infinite cylindrical pipe, centered on the z axis, with grounded side walls. One

end, which is aligned with the xy plane, has a cap that carries a potential VO = VO(s). The other end is

uncapped and lies at infinity. Use separation of variables to find a set of ordinary differential equations

that describe the potential inside the cylinder and the relationship between them. You do not need to

solve the diff. eqs.