ABSTRACT
The majority of field problems reduce either to the solution of Laplace’s equation or that of Poisson’s equation. Once a solution is found, it becomes a bone of contention whether the obtained solution is the only possible solution. The answer to this question is given by the uniqueness theorem, which is considered as a litmus test in all such cases. This chapter begins with the uniqueness theorem and explores its applicability and compatibility for the solutions of Laplace’s and Poisson’s equations. The domain of the uniqueness theorem is further extended to encompass the vector magnetic potential and Maxwell’s equations. This chapter also includes the discussion on Helmholtz’s theorem and the generalised Poynting theorem. A new concept of approximation theorems is also introduced and their usefulness for the Laplace equation, vector magnetic potential and eddy current equation is explored.
