Final answer:
The intensity of the force between the two original spheres becomes 3 F/8 after they share their charges with a third conducting sphere, due to the redistribution of electrical charge and Coulomb's Law which states that force is proportional to the product of the charges involved.
Step-by-step explanation:
When two identical conducting and insulated spheres are initially charged with equal amounts and repel each other with force F, sharing their charges with a third identical sphere reduces the individual charges on each of the original spheres. Initially, each sphere has a charge of q.
After the first contact with the uncharged sphere, the charge on the original sphere is halved to q/2, since charges distribute evenly.
When the previously uncharged sphere touches the second charged sphere, the charges will redistribute again, resulting in both the second and third spheres having a charge of q/4.
When the third sphere is removed from the system, the two original spheres are left with q/2 and q/4 respectively, summing up to q/2 + q/4 = 3q/4 for the total charge.
Since the force between two charges scales with the product of the charges involved, according to Coulomb's Law, and the distances in both cases remain the same, we are interested in the square of the total final charge on both spheres relative to the square of the initial charge: (3q/4)^2 = (9/16)q^2, which is 9/16 the initial force.
Thus, the new force between them is 3 F/8.