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Potential at a General Point Due to a Dipole

Consider two ...

Question

Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2} (r_{2} > r_{1})$ . If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is :

A

\frac{- r_{2}}{r_{1}} q

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B

Zero

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C

\frac{- r_{1}}{r_{2}} q

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D

- q

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Solution

The correct option is B $\frac{- r_{1}}{r_{2}} q$
Let, the change on the inner shell be $q^{'}$
Since the shell is grounded net electric potential will be zero.
So, $\frac{k q^{'}}{r_{1}} + \frac{k q}{r_{2}} = 0$ $(∵ r_{2} > r_{1})$
$\Rightarrow q^{'} = - \frac{\frac{K q}{r_{2}}}{\frac{K}{r_{1}}}$
$q^{'} = - (\frac{r_{1}}{r_{2}}) q$

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