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 Fb) 1/8 Fc) 1/2 Fd) 1/4 F

Answer: c) 1/4F

Explanation: In order to explain this result we must use the Coulomb force expression, that is:

F = (k*q1*q2) / d^2 where d is the distance between spheres, k a constant equal to 9*10^9N^2. m^2/C

after time each sphere lost haft of original charge and taking into account that F is directly proportional to charge of each sphere,

we have Fafter = (k*q1/2*q2/2) / d^2

then Fafter = (1/4) (k*q1*q2) / d^2 = (1/4) Finitial