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

Question

Quizplus · Accepted Answer

The electrostatic force between two charges is given by Coulomb's law: $ F = k \frac{q_1 q_2}{r^2} $. If each sphere loses half its charge, the new charges are $ q_1/2 $ and $ q_2/2 $. The new force is $ F' = k \frac{(q_1/2)(q_2/2)}{r^2} = \frac{1}{4} k \frac{q_1 q_2}{r^2} = \frac{1}{4} F $.

Two Identical Small Charged Spheres Are a Certain Distance Apart 2\sqrt { 2 }2​

Two Identical Small Charged Spheres Are a Certain Distance Apart $\sqrt { 2 }$