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Question

Charge Q, 2Q and 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 32
For 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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