Question

Two small identical metallic spheres A and B having + 2Q and - Q charges
respectively are kept r distance apart. They were found to attract each other
by a force F. If they are brought in contact and then separated to their
original locations, the electric force between them will be
(A) F/4, attractive
(B) F/4, repulsive
(C) F/8, attractive
(D) F/8, repulsive

Answer 1

Answer:

They must both have the same final charge because they will both be at the same potential.

If charge q is transferred from the positive sphere to the negative sphere then

(2 Q - q) + (-Q + q) = 2 Qf     where Qf is the final charge on each sphere

So Qf = Q / 2

Initial force proportional to 2 Q * Q  = 2 Q^2     attractive

final force proportional to (Q / 2)^2 = Q^2 / 4     repulsive

So Ff = F / 8  and the force is repulsive

Answer 2

Answer:

(C) F/8, repulsive

Explanation:

(2 Q - q) + (-Q + q) = 2 Qf     where Qf is the final charge on each sphere

So Qf = Q / 2

Initial force proportional to 2 Q * Q  = 2 Q^2     attractive

final force proportional to (Q / 2)^2 = Q^2 / 4     repulsive

So Ff = F / 8  and the force is repulsive