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Q.

Two conducting spheres of radii r₁ and r₂ have same electric field near their surfaces. The ratio of their electric potential is

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a

${r_{1}}^{2} / {r_{2}}^{2}$

b

${r_{2}}^{2} / {r_{1}}^{2}$

c

$r_{1} / r_{2}$

d

$r_{2} / r_{1}$

answer is D.

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Detailed Solution

$E = \frac{1}{4 {πε}_{0}} \times \frac{q_{1}}{r_{1}^{2}} and E = \frac{1}{4 {πε}_{0}} \times \frac{q_{2}}{r_{2}^{2}} ∴ \frac{V_{1}}{V_{2}} = \frac{\frac{1}{4 {πε}_{0}} \times \frac{q_{1}}{r_{1}}}{\frac{1}{4 {πε}_{0}} \times \frac{q_{2}}{r_{2}}} = \frac{r_{2}}{r_{1}}$

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