Two conducting spherical shells are concentric. One shell has an inner radius of

Question

Two conducting spherical shells are concentric. One shell has an inner radius of 3.0cm and an outer radius of 4.0cm, while the second shell has an inner radius of 6.0cm and an outer radius of 8.0cm. The smaller shell has a charge of 2.0nC and the larger shell has a charge of -6.0nC.

(a) How much charge is on the inner and outer surfaces of each sphere?
(b) At what potential is each sphere?
(c) If the two shells were connected by a wire, how much charge would there be on the inner and outer surfaces of each shell?
(d) At what potential are the two shells now?

Explanation / Answer

a) small shell - all charge on outer surface 2 nC large shell - charge of -2 nC on inner surface (balances small shell) charge of -4 nC left on outer surface b) V(small) = k * 2 * 10E-9 / .04^2 where k = 9 * 10E9 V(large = k * (-4 * 10E-9) / .08^2 c) all charge -4 nC now on outer surface of large shell - this is "Faraday's Ice Pail" experiment - no electric fields can exist inside the outer surface of the large shell otherwise a current would flow d) V = k * (-4 * 10E-9) / .08^2 (total charge enclosed is -4 nC)

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