Question

A charge q is placed at the centre of the line joining two exactly equal positive charges Q. The system of three charges will be in equilibrium, if q is equal to

• A. - Q
• B. Q/2
• C. Q/4
• D. + Q

Answer 1

Answer: (C)

For equilibrium of charge Q, the force of repulsion due to similar charges Q should be balanced by the force of attraction due to charge q and
$\frac{1}{4\pi {\epsilon }_0}\times \frac{Qq}{(r/2{)}^2}+\frac{1}{4\pi {\epsilon }_0}\times \frac{Q^2}{r^2}=0$
or $4\times \frac{Q}{r^2}q=-\frac{Q^2}{r^2}$ or $4q=-Q$ or $q=-\frac{Q}{4}$.