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Question

In the figure shown, a spherical conductor has a spherical cavity. A charge Q is placed as shown in figure. Then, choose the correct statement(s):


A
Charge distribution on S2 is uniform and on S1 is non-uniform.
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B
Charge distributions on S1 and S2 are non-uniform.
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C
Charge distributions on both S1 and S2 are uniform.
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D
Charge distribution on S1 is uniform and on S2 is non-uniform.
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Solution

The correct option is A Charge distribution on S2 is uniform and on S1 is non-uniform.
Due to the induction process, the +Q charge placed inside the cavity induces Q charge on the surface S1. Since the charge is not placed at the geometrical centre of the cavity, so the charge distribution on S1 is non-uniform. [in order to make the electric field at every point in the cavity equal to zero.

However, since the electric field doesn't pass through the conductor, charge distribution on the outer surface is not influenced by Q. Hence, charge distribution on S2 will be uniform, independent of the location of Q.
Option (b) is correct.
Why this question?

Charge distribution on the inner surface is uniform only if the cavity is spherical and the charge is placed at the geometric center.

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