Physics - Electrostatics Question with Solution | TestHub

By Coulomb's law,

When charge Q is divided into two charges q and Q - q

$F=\frac{1}{4\pi {\epsilon }_0} .\frac{q.\left(Q-q\right)}{r^2}$

The value of$q$

$F_{max}=\frac{1}{4\pi {\epsilon }_0} .\frac{\frac{Q}{2}\left(Q-\frac{Q}{2}\right)}{r^2}$

(putting$q=\frac{Q}{2}$for the maximum force)

$=\frac{1}{4\pi {\epsilon }_0} .\frac{\frac{Q}{2}\left(\frac{Q}{2}\right)}{r^2}$

$=\frac{1}{4\pi {\epsilon }_0}.\frac{\frac{Q^2}{4}}{r^2}$

$=\frac{1}{4\pi {\epsilon }_0} .\frac{Q^2}{4r^2}$

$=\frac{1}{4\pi {\epsilon }_0} .\frac{{\left(\frac{Q}{2}\right)}^2}{r^2}$

So, option$\frac{Q}{2}$is correct.