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Question

# Charge Q, 2Q and âˆ’Q are given to three concentric conducting spherical shells A, B and C respectively as shown in figure. The ratio of charges on the inner and outer surfaces of shell C will be

A
+34
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B
34
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C
32
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D
32
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Solution

## The correct option is D −32For the given conducting spherical shells the charges Q, 2Q,−Q on shells A, B and C will reside at their outer surface. Let E is electric field and dA is elemental Gaussian surface. For shell A The charge Q will appear at the outer surface of the shell and there will be no charge in the inner surface. For shell B Draw an imaginary Gaussian surface inside the shell B and apply Gauss law. ∮→E.−→dA=qenϵ0 ⇒→E=0, qen=0 The charge qen will be zero only if the inner surface of shell B will induce −Q charge due to Q charge on the outer surface of shell A. The charge on outer surface =2Q For shell C Draw an imaginary Gaussian surface inside the shell C and apply Gauss law. ∮→E.−→dA=qenϵ0 ⇒→E=0, qen=0 Again the charge qen will be zero only if the inner surface of shell C will induce −3Q charge due to (2Q+Q) charge inside the shell. The charge on outer surface =−Q+3Q=2Q Now the ratio of charge =−3Q2Q=−32

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