Question

Two concentric spheres of radii $R$ and $2R$ are charged. The inner sphere has a charge of $1\mu \text{C}$ and the outer sphere has a charge of $2\mu \text{C}$ of the same sign. The potential is $9000\text{V}$ at a distance $3R$ from the common centre. The value of $R$ is

• A. $4\text{m}$
• B. $1\text{m}$
• C. $2\text{m}$
• D. $3\text{m}$

Answer 1

The correct option is B $1\text{m}$

Given:
$Q_1={10}^{-6}\text{C};Q_2=2\times {10}^{-6}\text{C}$


We know that the formula of potential at outside the shell is given by,
$V=\frac{kQ}{r}$

$\therefore V_P=V_1+V_2$

$\Rightarrow V_p=\frac{9\times {10}^9\times 1\times {10}^{-6}}{3R}+\frac{9\times {10}^9\times 2\times {10}^{-6}}{3R}$

$\Rightarrow R=\frac{9\times {10}^9\times {10}^{-6}}{9000}$

$\Rightarrow R=1\text{m}$

Therefore, option $\left(a\right)$ is correct.

Why this question? Concept- Electric potential at any point $\text{P}$ outside the shell is $V=\frac{kq}{r}$ ( $r=$ distance of the point from the centre)