Question: (a) Solve the Dirichlet problem for the Laplace equation in the interior of a unit sphere Au =0, p 0+ (13) u is bounded as

(a) Solve the Dirichlet problem for the Laplace equation in the interior of a unit sphere Au =0, p 0+ (13) u is bounded as o -> 0 + and 0 -> *- (14) where A denotes the Laplacian operator in cartesian coordinates, u = u(p, 0, $) is an electrostatic potential and (p, 0, ) are spherical coordinates. (b) write the solution in cartesian coordinates

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