# Two conducting spheres of radii r1 and r2 have same electric fields near their surfaces. The ratio of their electric potentials is

Q: Two conducting spheres of radii r1 and r2 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) $\large \frac{r_2}{r_1}$

Ans:(c)

Sol: $\large E_1 = E_2$

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

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

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

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