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  4. Two point charges A and B of magnitude +8 × 10-6 C and -8 × 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 × 104 NC -1. The distance 'd' between the point charges A and B is:

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Q. 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 $6.4 \times 10^{4} NC ^{-1}$. The distance '$d$' between the point charges $A$ and $B$ is:

JEE MainJEE Main 2022Electric Charges and Fields

Solution:

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$E _{0}=2 \times \frac{ Kq }{( d / 2)^{2}}$
$\Rightarrow E _{0}=8 \frac{ Kq }{ d ^{2}}$
$\Rightarrow d ^{2}=\frac{8 \times 9 \times 10^{9} \times 8 \times 10^{-6}}{6.4 \times 10^{4}}$
$d =3 \,m$