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Excess Pressure in Bubbles

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 :

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

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Zero

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

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- q

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Solution

The correct option is C $\frac{- r_{1}}{r_{2}} q$
Let the charge on inner shell be $Q$ .
Since it is grounded, the potential of the shell must be zero due to both charge on inner shell and that on outer.
Hence $\frac{k Q}{r_{1}} + \frac{k q}{r_{2}} = 0$
$⟹ Q = - \frac{r_{1}}{r_{2}} q$

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