A conducting sphere of radius R carries charge Q. It is surrounded concentrically by an initially neutral conducting spherical shell with inner radius 2R and outer radius 3R. The potential of the inner sphere relative to infinity is:
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Question

A conducting sphere of radius R carries charge Q. It is surrounded concentrically by an initially neutral conducting spherical shell with inner radius 2R and outer radius 3R. The potential of the inner sphere relative to infinity is:

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G1 Physics · Accepted Answer

The shell acquires -Q on its inner surface and +Q on its outer surface. Potential at the inner sphere is the sum: Q/(4πε₀R) - Q/[4πε₀(2R)] + Q/[4πε₀(3R)]. Therefore V=Q/(4πε₀)(1/R-1/(2R)+1/(3R)).