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Principle of Superposition

Two small con...

Question

Two small conductors A and B are given charges $q_{1}$ and $q_{2}$ respectively. Now they are placed inside a hollow metallic conductor C carrying and charge Q. If all the three conductors A, B and C are connected by a conducting wire as shown, the charges on A, B and C will be respectively

A

\frac{q_{1} + q_{2}}{2}, \frac{q_{1} + q_{2}}{2}, Q

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B

\frac{Q + q_{1} + q_{3}}{3}, \frac{Q + q_{1} + q_{2}}{3}, \frac{Q + q_{1} + q_{2}}{3}

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C

\frac{q_{1} + q_{2} + Q}{2}, \frac{q_{1} + q_{2} + Q}{2}, 0

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D

0, 0, Q + q_{1} + q_{2}

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Solution

The correct option is D $0, 0, Q + q_{1} + q_{2}$
When sphere A and B is connected to the metallic shell by a wire, the all charges will reside on the outer surface of the metallic shell.
Thus, Charge on A and b become 0 and charge on C $= Q + q_{1} + q_{2}$

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