A pair of thin concentric conducting spherical shells, of radii a and b, are arranged as shown. The inner shell carries charge +q while the total charge on the outer shell is +Q. Give answers in terms of these quantities.
a. Find the magnitude of the E-field E(r) where r I, r > b ; II, a < r < b ; III, r < a .
Ans: I:E=k(Q+q)/r2; II:E=kq/r2; III:E=0.
b. Write the formula for the potential in those three regions, taking V(?) = 0 .
Ans: I: V = k(Q + q)/r; II: V = kQ/b + kq/r; III: V = kQ/b + kq/a .
c. Suppose small holes are drilled through the spheres along the dotted line in the figure, and an electron (charge –e) is released from rest in the hole at the top of the outer shell (distance r = b from the center). What is the kinetic energy of the electron when it is at the center of the spheres?