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 leaks off of 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) 1/4 F.
D) 1/2 F.

Question

Quizplus · Accepted Answer

The electrostatic force between two charged spheres is given by Coulomb's law:

F = kq1q2/r^2

where k is the Coulomb constant, q1 and q2 are the charges on the spheres, and r is the distance between them.

If each sphere loses half its initial charge, the new charges on the spheres will be q1/2 and q2/2, respectively. The distance between them, however, remains the same.

Using the new charges in Coulomb's law, the new electrostatic force between the spheres is:

F' = k(q1/2)(q2/2)/r^2 = kq1q2/4r^2 = F/4

Thus, when each sphere has lost half its initial charge, the magnitude of the electrostatic force between them will be 1/4 of the initial force.

Therefore, the best choice is C) 1/4 F.

Two Identical Small Charged Spheres Are a Certain Distance Apart,and