2008 AP Physics C E&M #1a?

Question

I don't know where to start, please help.

A metal sphere of radius a contains a charge +Q and is surrounded by an uncharged, concentric, metallic shell

of inner radius b and outer radius c, as shown above. Express all algebraic answers in terms of the given

quantities and fundamental constants.

(a) Determine the induced charge on each of the following and explain your reasoning in each case.

i. The inner surface of the metallic shell

ii. The outer surface of the metallic shell

Actual exam w/ picture:

http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_em_frq.pdf

Answer 1

Create a Gaussian surface within the outer metal shell and apply Gauss's theorem ∫e0*E*dS = ∫q*dV.  The field E inside the conductive shell is zero, so the total charge inside the Gaussian surface is zero.  Charges will only reside on the surface of metal objects, so the charge on the inner surface of the shell must be -Q.   The shell is uncharged, so its inner and outer surface charges must be equal and opposite, so the outer surface charge is +Q