Question

Proof of uniqueness theorem electrostatics

Answer 1

Solution of Laplace’s and Poisson’s Equation can be obtained in a number of ways. For a given set of boundary conditions, if we can find a solution to Poisson’s equation ( Laplace’s equation is a special case), we first establish the fact that the solution is a unique solution regardless of the method used to obtain the solution. Uniqueness theorem thus can stated as: