Q. Two point charges $ +5\mu C $ and $ -2\mu C $ are kept at a distance of $1\,m$ in free space. The distance between the two zero potential points on the line joining the charges is
Solution:
Let the potential be zero at P and Q. Then solving for
$ {{x}_{1}} $
$ \frac{k\times 5}{{{x}_{1}}}=\frac{2k}{(1-{{x}_{1}})} $
$ {{x}_{1}}=\frac{5}{7} $
Similarly, $ \frac{k\times 5}{1+{{x}_{2}}}=\frac{k\times 2}{{{x}_{2}}} $
$ \therefore $ $ {{x}_{2}}=\frac{2}{3} $
Separation $ PQ=\left( 1-\frac{5}{7} \right)+\frac{2}{3} $
$ =\frac{20}{21} $
