Find the electric field a distance z above the center of a flat circular disk of radius R, which carries a uniform suface charge sigma, s . Derive Poisson's equation for the electric potential. Find the potential inside the outside of a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Compute the gradient of your potential, check that it yields the correct field.
E is perpendicular to the surface, just outside a conductor.
Derive the potential and surface charge for a point charge in the vicinity of an infinite grounded conducting sheet. Also derive the magnitude and location of the image charge. Show that the energy density in a dielectric is given by D . Derive the Clausius-Mossotti relation. Given a vector potential, calculate B .