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} $
Click to See Answer :
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} $