Question 92 of 311

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

A$2m$B$3m$C$1m$D$4m$

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Answer: (B) $3m$

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 $=\dfrac{kq}{{\left(\dfrac{d}{2}\right)}^{2}}+\dfrac{kq}{{\left(\dfrac{d}{2}\right)}^{2}}$
$\Rightarrow 6.4\times {10}^{4}=2\times \left[9\times {10}^{9}\times \dfrac{\left(8\times {10}^{-6}\right)}{{d}^{2}}\times 4\right]$
$\Rightarrow d=3m$