12. ( 16 points) A conducting spherical shell with inner radius a and outer radius b has a total charge of +3Q. The shell is insulated from its surroundings. 3) 13) Sketch the shell in two dimensions, indicating where its charge is distributed. What is the electric eld inside the shell? A negative charge -Q is now placed at the center of the shell. Derive the expression for the electric eld and indicate the direction of the electric eld vector in terms of the distance r om the center for the following regions. i) rb Extra credit: What is the surface charge density on the inner and outer surfaces of the shell? (Hint: you should know the amount of charge on its surfaces already.)