Question

If the force between two charged objects is to be left unchanged even though the charge on one of the object is halved keeping the other same, the original distance (d) of separation should be changed to :

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

Answer 1

Answer: (C)

$\frac{d}{\sqrt{2}}$

initial force $=\frac{k{q}_1{q}_2}{d^2}$
Now $q_1$ is halved, let final distance be x for same force to act
$\Rightarrow \frac{k\left(\frac{q_1}{2}\right)\left(q_2\right)}{x^2}=\frac{k{q}_1{q}_2}{d^2}$

$\Rightarrow \frac{1}{\sqrt{2}x}=\frac{1}{d}$

$\Rightarrow x=\frac{d}{\sqrt{2}}$