Question

If the force between two charged objects separated by a distance d is to be left unchanged even though the charge on one of the objects is halved, keeping other the same, the new distance of separation becomes :

• A. $d\sqrt{2}$
• B. $\frac{d}{\sqrt{2}}$
• C. $\frac{\sqrt{2}}{d}$
• D. $2d$

Answer 1

The correct option is B $\frac{d}{\sqrt{2}}$

According to coulomb's inverse square law,

$F=\frac{k{q}_1{q}_2}{d^2}$

If charge on one of the objects is halved, but force remains unchanged,

$F=\frac{\frac{k{q}_1}{2}{q}_2}{{d_1}^2}$

Hence, $\frac{q_1}{d^2}=\frac{\frac{q_1}{2}}{{d_1}^2}$

$\therefore d_1=\frac{d}{\sqrt{2}}$