Reference no: EM132106036

Question: A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius r_b. 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 < r_a. (Hint: the net potential is the sum of the potentials due to the individual spheres.)

b) Calculate the potential V(r) for r_a< r < r_b.

c) Calculate the potential V(r) for r > r_b.

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

e) Use the equation E_r=- \frac{\partial V}{\partial r} and the result from part (b) to find the electric field at any point between the spheres (r_a < r < r_b).

f) Use the equation E_r=- \frac{\partial V}{\partial 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>r_b.

g) Suppose the charge on the outer sphere is not -q but a negative charge of different magnitude, say -Q. Find the potential of the inner sphere with respect to the outer.

h) Suppose the charge on the outer sphere is not -q but a negative charge of different magnitude, say -Q. Find the electric field at any point between the spheres (r_a < r < r_b).