Answer: A metal sphere with radius ra is supported on an

Chapter 23, Problem 23.41

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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. (a) Calculate the potential V1r2 for (i) r 6 ra; (ii) ra 6 r 6 rb; (iii) r 7 rb. (Hint: The net potential is the sum of the potentials due to the individual spheres.) Take V to be zero when r is infinite. (b) Show that the potential of the inner sphere with respect to the outer is Vab = q 4pP0 a 1 ra - 1 rb b (c) Use Eq. (23.23) and the result from part (a) to show that the electric field at any point between the spheres has magnitude E1r2 = Vab 11>ra - 1>rb2 1 r2 (d) Use Eq. (23.23) and the result from part (a) to find the electric field at a point outside the larger sphere at a distance r from the center, where r 7 rb. (e) Suppose the charge on the outer sphere is not -q but a negative charge of different magnitude, say -Q. Show that the answers for parts (b) and (c) are the same as before but the answer for part (d) is different