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Potential and Potential Energy Relation

What is the p...

Question

What is the potential of the inner sphere? What is the potential at r = 0?

A

\frac{Q_{2}}{R_{2}} + \frac{Q_{1}}{R_{1}}

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B

\frac{Q_{2}}{R_{2}} - \frac{Q_{1}}{R_{1}}

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C

\frac{Q_{2} - Q_{1}}{R_{1}}

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D

\frac{Q_{2} + Q_{1}}{R_{1}}

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Solution

The correct option is A $\frac{Q_{2}}{R_{2}} + \frac{Q_{1}}{R_{1}}$
Potential of inner sphere due to charge on inner sphere $= V_{1} = \frac{k_{e} Q_{2}}{R_{2}}$

Potential of inner sphere due to charge on outer sphere $= V_{2} = \frac{k_{e} Q_{1}}{R_{1}}$

Hence, total potential of outer sphere $= V = V_{1} + V_{2}$

$⟹ V = k_{e} (\frac{Q_{1}}{R_{1}} + \frac{Q_{2}}{R_{2}})$

The potential at centre that is at $r = 0$ is same as that of the inner sphere that is $V$ .

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