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)1/4 F.
D)1/2 F.

Question

Quizplus · Accepted Answer

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

F = k*(q1*q2)/r^2

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

Since the spheres are identical, their charges will decrease by the same factor as they lose charge. Let q be the original charge on each sphere. When each sphere has lost half its charge, their new charges will be q/2.

Plugging this into Coulomb's law, we get:

F' = k*((q/2)*(q/2))/r^2 = k*q^2/(4*r^2)

The ratio of the new force to the original force is:

F'/F = (k*q^2/(4*r^2))/(k*q^2/r^2) = 1/4

Therefore, the magnitude of the electrostatic force when each sphere has lost half its charge will be 1/4 of the original force, which is choice C.

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