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/ F

Question

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/ F

Quizplus · Accepted Answer

The electrostatic force between two charged spheres is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them:

F = kQ1Q2/d^2

where k is a constant of proportionality, Q1 and Q2 are the charges on the spheres, and d is the distance between them.

Since the spheres are identical and initially have the same charge, we can assume that Q1 = Q2 = Q. When each sphere has lost half its initial charge, its new charge is Q/2. The distance between the spheres remains the same, so we can calculate the new force using these values:

F' = k(Q/2)(Q/2)/d^2
F' = kQ^2/4d^2
F' = F/4

Therefore, the magnitude of the electrostatic force on each sphere when each has lost half its initial charge is 1/4 of the initial force, or choice (C).

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