A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge −q on the outer spherical shell. Take V to be zero when r is infinite.

a. Calculate the potential V(r) for r
b. Calculate the potential V(r) for ra
c. Calculate the potential V(r) for r>rb

d. Find the potential of the inner sphere with respect to the outer.

Use the equation Er=−∂V∂r and the result from part (b) to find the electric field at any point between the spheres (ra

Use the equation Er=−∂V∂r and the result from part (c) to find the electric field at a point outside the larger sphere at a distance r from the center, where r>