Question

A conducting wire connects two charged conducting spheres of radii r₁ and r₂ such that they attain equilibrium with respect to each other. The distance of separation between the two spheres is very large as compared to either of their radii.

The ratio of the magnitudes of the electric fields at the surfaces of the spheres of radii r₁ and r₂ is:

Options

• ${\displaystyle \frac{r_1}{r_2}}$

• ${\displaystyle \frac{r_2}{r_1}}$

• ${\displaystyle \frac{r_2^2}{r_1^2}}$

• ${\displaystyle \frac{r_1^2}{r_2^2}}$

Answer 1

${\displaystyle \frac{r_2}{r_1}}$

Explanation:

In the state of equilibrium, 

The potential on the surface of bigger sphere = the potential at the surface of the smaller sphere

${\displaystyle \frac{k{q}_1}{r_1}=\frac{k{q}_2}{r_2}\Rightarrow \frac{q_1}{q_2}=\frac{r_1}{r_2}}$

${\displaystyle \therefore \frac{E_1}{E_2}=\frac{q_1}{q_2}\frac{r_2^2}{r_1^2}=\frac{r_1}{r_2}\cdot \frac{r_2^2}{r_1^2}=\frac{r_2}{r_1}}$