Two small charged objects repel each other with a force F when separated by a di

Question

Two small charged objects repel each other with a force F when separated by a distance D. If the charge on each object is reduced to 1/4th of their original charge and the distance between them is reduced by ½, the force between them becomes:

a. F/16

b. F/8

c. F/4

d. F/2

e. F/4

The moving bar of a positively charged electroscope diverges further away from its vertical rigid post when an object is brought near the top plate of the electroscope. The object must be a. a conductor b. an insulator c. negatively charged d. uncharged e. positively charged Two uncharged metal spheres, X and Y are in contact. A negatively charged rod is brought close to, but not touching, X as shown. The two spheres are then slightly separated with the charged rod still in place as shown. The rod is then removed to some distant location. As a result, the spheres are charged a. both neutral b. both positive c. both negative d. X negative and Y positive e. X positive and Y negative insulating supports

Explanation / Answer

Initially,

Distance = d

Charge = q

F = (kq^2)/(d/2)

Now,later on the charge on each object is reduced to 1/4th of their original charge and the distance between them is reduced by ½, the force between them becomes:

Distance (d1) = d/2

Charge(q1)= q/4

Then, in that case

F1 = [(1/4)2*2]/d = F/8

Therefore, (C) is the correct option.

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