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Charge Behaviour

A point charg...

Question

A point charge Q is located at the center of the hollow spherical conductor of inner radius $R_{1}$ and outer radius $R_{2}$ , the conductor being uncharged initially. The potential at the inner surface will be

K Q [\frac{1}{R_{1}} + \frac{1}{R_{2}}]

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K Q [\frac{1}{R_{1}} - \frac{1}{R_{2}}]

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K Q [\frac{1}{R_{2}} - \frac{1}{R_{1}}]

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None of these

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Solution

The correct option is A $K Q [\frac{1}{R_{1}} + \frac{1}{R_{2}}]$
Given that,
Inner radius $= R$
Outer radius $= R_{2}$
Now, Potential dueto $R_{1} = \frac{K Q}{R_{1}}$
Potential due to $R_{2} = \frac{K Q}{R_{2}}$
Total potential $= \frac{K Q}{R_{1}} + \frac{k Q}{R_{2}}$
Potential $= K Q [\frac{1}{R_{1}} + \frac{1}{R_{2}}]$

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