A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge −3Q, the new potential difference between the same two surfaces is :
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Correct option is A)
The electric field in between the shell and sphere is E.πx2=ϵ0Qen=ϵ0Q (using Gauss's law) E=4πϵ0x2Q The potential difference between the shells is dV=Vr−VR=∫rREdx=∫rR4πϵ0x2Qdx=4πϵ0Q(1/r−1/R) Thus, V=4πϵ0Q(1/r−1/R) As the potential difference between solid sphere and hollow shell depends on the radii of two spheres and charge on the inner sphere, Since the two values have not changed, potential difference does not change. Hence the potential difference remains V.
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