M. Fabbrichesi , SISSA

5. Poisson equation

The first part of this lesson presents the solution of the Poisson equation through a Green's function approach. Dirichlet and Neumann boundary conditions are discussed (Jackson sect. 1.8, 1.9 and 1.10). Next, the method of the images is applied to find out the potential generated by a charge at a distance a from a plane put at ground (zero potential). As further example, it is also shown how to find the potential generated by a charge with the constraint to be zero on a spherical surface at a distance x from the charge. Finally a few mathematical properties of analytic functions are discussed for the solution of two-dimensional electrostatic problems.