Question

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

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

Answer 1

Answer: (C)

$V_{A}-V_{B}=\frac{k q}{r}-\frac{k q}{3 r}=V$
$\frac{k q}{r}\times \, \frac{2}{3}=V$
$E_{B}=\frac{k q}{\left(3 r\right)^{2}}=\frac{3}{2}\frac{V r}{\left(3 r\right)^{2}}=\frac{3 V r}{2 \times 9 \times r^{2}}=\frac{V}{6 r}$