Spring 2007 4 Em

A sphere of radius R has volume charge density $\rho = K r^n$, for some constants K and n. The region r > R is filled with a conductor (all the way to infinity).

(a) Find the volume charge density $\rho$ in the region r > R, inside the conductor, and the surface charge density at r = R.

(b) Find the electric field E everywhere, i.e. for r < R and for r > R.

(c) Find the potential $\phi$ everywhere, taking $\phi$ to vanish at infinity.

(d) How much energy is stored in this system?

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