We did more examples on the solution of electrostatic problems with the method of images. In particular the energy balance in the electrostaticfield was discussed following the example of the Van der Graff type accelerator

We discussed solutions of the Laplace and Poisson equations in terms of polynomial and functional expansions. We considered spherical boundaries and therefore we wrote the equations above in spherical coordinates.

We first discussed solutions to the homogeneous equation for problems with azymuthal symmetry: these solutions can be written as a series of Legendre Polynomials.

We are on Sections 3.1, 3.2, 3.3 of Jackson.

1) Using the method of images find the electric field at any point in space for a charge q placed at coordinates (x,y)=(a,b) between two grounded conducting planes forming a 90 deg. angle. What is the field on the surface of each plane?

2) A disk of radius a and surface charge density sigma = K r/a lies in the xy plane with its center at the origin. Using delta functions express the volume density in: a) cylindrical coordinates; b) spherical coordinates.

Due next Thursday!