Question

Two charged spheres having radii a and b are joined with a wire then the ratio of electric field $\frac{E_a}{E_b}$ on their surface is?

• A. a/b
• B. b/a
• C. ba
• D. None of these

Answer 1

The correct option is B b/a

When the two spheres are connected by a wire, then both of them acquire the same potential say $V$.

We also know that the electric field on the surface of a sphere $E=\frac{Q}{4\pi {ϵ}_o{r}^2}$

and potential on the surface is given by $V=\frac{Q}{4\pi {ϵ}_{o}r}$

$⟹E=\frac{V}{r}$

Here, V is constant , hence $E\propto \frac{1}{r}$

$⟹\frac{E_a}{E_b}=\frac{b}{a}$