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Q.

Two spheres of radii $R_{1}$ and $R_{2}$ respectively are charged and joined by a wire. The ratio of electric fields on the spheres is

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a

$\frac{R_{1}^{3}}{R_{2}^{3}}$

b

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

c

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

d

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

answer is C.

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Detailed Solution

as $V = \frac{K q}{R} \Rightarrow q \propto R$ as potential is same for both

$E \propto \frac{q}{R^{2}} \Rightarrow E \propto \frac{R}{R^{2}} \Rightarrow E \propto \frac{1}{R}$

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

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