Problem # 1
Show that the electrostatic energy stored in the electric field of a charge distribution is expressed
as $(\epsilon_0/2) \int E^2 d\tau$, where the integration is over all space.
Problem # 2
Find the electrostatic energy stored in the following two systems: (i) a non-conducting sphere of
radius R with a charge Q uniformly distributed within its volume. (ii) A conducting sphere of radius
R with total charge Q.
Problem # 3
Find the capacitance of two concentric spherical metal shells, with radius a and b.
Problem # 4
Find the capacitance per unit length of two coaxial metal cylindrical tubes of radius a and b.
Problem # 5
A conical surface (an empty ice-cream cone) carries a uniform surface charge $\sigma$. The height
of the cone is h, as is the radius of the top. Find the potential difference between point a
(the vertex) and b (the center of the top).
