Question

Two identical small charged spheres are a certain distance apart, and each initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually diminishes on both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be
(A) 1/16 F
(B) 1/8 F
(C) 1/2 F
(D) 1/4 F

Answer 1

Answer:

New force, $F'=\dfrac{1}{4}F$

Explanation:

The electrostatic force between two spheres is given by :

$F=\dfrac{kq_1q_2}{r^2}$

According to given condition, each of the spheres has lost half its initial charge, new force is given by :

$F'=\dfrac{kq_1/2q_2/2}{r^2}$

$F'=\dfrac{1}{4}\times \dfrac{kq_1q_2}{r^2}$

$F'=\dfrac{1}{4}F$

So, the new force becomes (1/4)th of the initial force. Hence, the correct option is (d).