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Standard XII

Physics

Potential Energy of Two Point Charges

A spherical m...

Question

A spherical metal shell $A$ of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{B} (< R_{A})$ are kept far apart and each is given charge $+ Q$ . Now they are connected by thin metal wire. Then:
(Here, $Q_{A}$ and $Q_{B}$ are the final charges on the spheres $A$ and $B$ respectively)

Q_{A} < Q_{B}

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Q_{A} = Q_{B}

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Q_{A} > Q_{B}

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Data insufficient

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Solution

The correct option is C $Q_{A} > Q_{B}$
In the steady state the potential of both the spheres will be same.
i.e. $V_{A} = V_{B}$

$\Rightarrow \frac{k Q_{A}}{R_{A}} = \frac{k Q_{B}}{R_{B}}$

Or, $\frac{Q_{A}}{Q_{B}} = \frac{R_{A}}{R_{B}}$

As, $R_{B} < R_{A}$ we get $Q_{A} > Q_{B}$ .

Therefore, option $(c)$ is the correct answer.

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Potential Energy of Two Point Charges

Standard XII Physics

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A spherical metal shell A of radius RA​ and a solid metal sphere B of radius RB(<RA) are kept far apart and each is given charge +Q. Now they are connected by thin metal wire. Then: (Here, QA and QB are the final charges on the spheres A and B respectively)

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(Here, $Q_{A}$ and $Q_{B}$ are the final charges on the spheres $A$ and $B$ respectively)