Two isolated concentric, conducting spherical shells have radii R and 2R and uniform charges q and 2q respectively. If $V_{1}$ and $V_{2}$ are potentials at points located at distances $3 R$ and $\frac{R}{2}$ respectively from the centre of shells. Then the ratio of $(\frac{V_{2}}{V_{1}})$ will be..

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$\frac{1}{2}$

answer is B.

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Detailed Solution

$For point, r = \frac{R}{2}$

$V_{1}$ = Potential of surface radius R+ Potential of surface radius 2R

$= \frac{kq}{R} + \frac{k 2 q}{2 R} = \frac{2 kq}{R}$

For point r = 3R ,

$V_{2}$ = Potential due to charges q and 2q assumed to be concentrated at centre

$= \frac{k (3 q)}{3 R} = \frac{kq}{R}$

$so ratio \frac{V_{1}}{V_{2}} = 2$

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