1 (20 min, Electrostatics in vacuum)
Using Gauss's law, calculate the capacitance of
(a) two concentric conducting spheres with radii a, b (b>a)
(b) two concentric conducting cylinders of length L, large compared to their radii a, b (b>a)
4 (20 min, Electrostatics in vacuum)
Find the potential at any point in space due to a total charge q uniformly distributed around a circular ring of radius R, located on the z-axis with center at z=b.
5 (30 min, Electrostatics in vacuum)
Consider a hollow grounded sphere of radius b with a concentric ring of charge of radius a(<b) and total charge Q. The ring of charge is located in the x-y plane. (a) Express the charge density using Dirac delta function.
(b) Find the Green function.
(c) Find the potential φ inside the sphere.
6 (30 min, Electrostatics in vacuum)
Find the general solution of Laplace's equation in cylindrical coordinates, assuming there is no dependence on z (cylindrical symmetry).