Q70 / 90 · JEE Main 2022 (28 Jun Shift 2) · Physics

Two point charges $A$ and $B$ of magnitude $+ 8 \times 10^{- 6} C$ and $- 8 \times 10^{- 6} C$ respectively are placed at a distance $d$ apart. The electric field at the middle point $O$ between the charges is $6.4 \times 10^{4} N C^{- 1}$ . The distance ' $d$ ' between the point charges $A$ and $B$ is

Solution

Direction of electric field at mid-point due to both charge will be in same direction, which is towards right.

Therefore, $E$ at mid-point $= \frac{k q}{{(\frac{d}{2})}^{2}} + \frac{k q}{{(\frac{d}{2})}^{2}}$

$\Rightarrow 6.4 \times 10^{4} = 2 \times [9 \times 10^{9} \times \frac{(8 \times 10^{- 6})}{d^{2}} \times 4]$

$\Rightarrow d = 3 m$

Hence, the correct answer is option: 'B'.