Q: Two conducting spheres of radii r_{1} and r_{2} have same electric fields near their surfaces. The ratio of their electric potentials is:

(a) $\large \frac{r_1^2}{r_2^2} $

(b) $\large \frac{r_2^2}{r_1^2} $

(c) $\large \frac{r_1}{r_2} $

(d) $\large \frac{r_2}{r_1} $

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Ans: (c)

Sol: $\large E_1 = E_2 $

$\large \frac{1}{4\pi\epsilon_0} \frac{q_1}{r_1^2} = \frac{1}{4\pi\epsilon_0} \frac{q_2}{r_2^2} $

$\large \frac{q_1}{q_2} = \frac{r_1^2}{r_2^2} $

$\large \frac{V_1}{V_2} = \frac{q_1}{q_2} \times \frac{r_2}{r_1} $

$\large \frac{V_1}{V_2} = \frac{r_1^2}{r_2^2} \times \frac{r_2}{r_1} = \frac{r_1}{r_2} $