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Question

# A charge +q is kept inside the cavity present in a solid conducting sphere, as shown in figure. If the sphere is given a charge Q, then total charge appearing on outer surface of sphere will be:

A
Qq
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B
Q
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C
(q+Q)
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D
Q+q
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Solution

## The correct option is D Q+qLet us consider a spherical Gaussian surface passing through region of conductor outside cavity. Electric field inside metal is always zero i.e E=0 On applying Gauss law, ∮→E.d→A=qenϵ0 Where, qen= charge enclosed by the Gaussian surface. dA= Elemental Gaussian surface area Thus, qen=0 This is only possible when a charge −q is induced at the inner surface of the cavity. The charge Q given to sphere will remain at its outermost surface and as per law of conservation of charge, +q will also appear on the outer surface of the sphere. The +q charge will quickly redistribute uniformly on the surface. ∴ Total charge appearing at outer surface =Q+q Hence, option (d) is correct. Why this question?Note: The electric field exists inside a cavity present in conductorif a charge is placed there. It is in accordance ofGauss's law(qen≠0,E≠0)

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