Question

A charged hollow metal sphere has a radius $r$. If the potential difference between its surface and a point at distance $3r$ from the centre is $V$, the electric intensity at a distance $3r$ from the centre is :-

• A. $\frac{V}{6R}$
• B. $\frac{V}{4R}$
• C. $\frac{V}{3R}$
• D. $\frac{V}{2R}$

Answer 1

The correct option is A $\frac{V}{6R}$

Given that:

$\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{q}{3r})=V$

or, $\frac{2q}{4\times 3\pi {ϵ}_{0}r}=V$

or, $\frac{q}{4\pi {ϵ}_{0}r}=\frac{3V}{2}$--------(i)

Now, $E=\frac{q}{4\pi {ϵ}_o\times (3r{)}^2}=\frac{3V}{2}\times \frac{1}{9r}=\frac{V}{6r}$