Two point charges placed a distance \( d \) apart in vacuum exert a force of magnitude \( F \) on each other. One of the two charges is doubled. To keep the magnitude of force same the separation between the charges should be changed to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \sqrt{2}\,d \)
The force between two point charges is given by Coulomb's law. Let the new separation be \( d' \).
\( \displaystyle F = \frac{k\,q_1 q_2}{d^{2}} \)
\( \displaystyle F = \frac{k\,(2q_1)\,q_2}{d'^{2}} \)
Equating the two forces for the same \( F \):
\( \displaystyle \frac{1}{d^{2}} = \frac{2}{d'^{2}} \;\Rightarrow\; d'^{2} = 2d^{2} \)
\( \displaystyle d' = \sqrt{2}\,d \)
The force is doubled by doubling one charge, so the separation squared must also double to bring it back.