Question

A charge Q is divided into two parts q and Q - q and separated by a distance R. The force of repulsion between them will be maximum when

• A. $q=Q/4$
• B. $q=Q/2$
• C. $q=Q$
• D. none of the above

Answer 1

Answer: (B)

$q=Q/2$

We have force of repulsion between the two charges,

$F_r=\frac{1}{4\pi {\epsilon }_0}\frac{q(Q-q)}{R^2}$

Now

(a)if $q=\frac{Q}{4}$, force $F=\frac{1}{4\pi {\epsilon }_0}\frac{3Q}{16}$

(b)if $q=\frac{Q}{2}$, force $F=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{4}$

(c) if $q=Q$, force $F=0$

Hence the force of repulsion between them will be maximum when $q=\frac{Q}{2}$.