Q: Two point sized identical spheres carrying charges q_{1} and q_{2} on them are separated by a certain distance. The mutual force between them is F. these two are brought in contact and kept at the separation. Now, the force between them is F’. Then $\large \frac{F’}{F} = \frac{(q_1 + q_2)^2}{4 q_1 q_2} $

Sol. When charges seperated by certain distance the force is given by

Then $\large F = \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r^2}$ … (i)

When charges brought in contanct and kept at the same distance the force is given by

$\large F’ = \frac{1}{4\pi \epsilon_0} \frac{(q_1 + q_2)^2}{4 r^2}$ …(ii)

From (i) and (ii) ;

$\large \frac{F’}{F} = \frac{(q_1 + q_2)^2}{4 q_1 q_2}$