A metal sphere of radius a is surrounded by a thick concentric metal shell (inner radius b, outer radius c). Neither the shell nor the sphere carries any charge, but there is a point charge +Q located inside an irregularly shaped cavity in the otherwise solid sphere as shown in the figure. The irregular cavity is not concentric with the sphere.
a) Sketch the induced charges on all the relevant surfaces.
b) What is the surface density of the charge on the outer surface of the sphere r=c?
c) What is the electric field where a<r<b?
c) What is the electric field where b<r<c?
The Attempt at a Solution
a) The positive charge within the irregular cavity will induce a negative charge on the surface of the cavity. This will in turn induce a positive charge on the surface of the sphere. A negative charge will be induced on the surface at b and a positive charge will be induced on the surface at c. This is illustrated in this image.
b) Q=σA where A=area of surface.
c) E=1/(4πε0) * Q/r^2
The total enclosed charge is Q.
d) This point is inside the metal shell so the E-field should be zero.
The enclosed charges are +Q from the sphere and -Q from the 'b' surface. The net charge is zero, so E= 1/(4πε0) * 0/r^2 == 0.
I'm using Griffith's E+M text.