Two isolated, charged conducting spheres of Radii $R_{1}$ and $R_{2}$ produce the same electric field near their surfaces. The ratio of electric potentials on their surfaces is

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$\frac{R_{1}}{R_{2}}$

$\frac{R_{2}}{R_{1}}$

$\frac{{R_{1}}^{2}}{{R_{2}}^{2}}$

$\frac{{R_{2}}^{2}}{{R_{1}}^{2}}$

answer is A.

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Detailed Solution

$E_{1} = E_{2} \Rightarrow \frac{K Q_{1}}{{R_{1}}^{2}} = \frac{K Q_{2}}{{R_{2}}^{2}} \Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{{R_{1}}^{2}}{{R_{2}}^{2}} \dots \dots \dots \dots \dots \dots \dots (1) \frac{V_{1}}{V_{2}} = \frac{Q_{1}}{Q_{2}} \frac{R_{2}}{R_{1}} \dots \dots \dots \dots \dots \dots (2) S o l v i n g e q u a t i o n s 1 a n d 2 \frac{V_{1}}{V_{2}} = \frac{R_{1}}{R_{2}}$