Question

Two identical spheres carry identical electric charges. If the spheres are set a distance d apart they repel one another with a force F. A third sphere, identical to the other two but initially uncharged is then touched to one sphere and then to the other before being removed. What would be the resulting force between the original two spheres?

(A) ¾ F 

(B) 5/8 F 

(C) ½ F 

(D) 3/8 F 

(E) ¼ F

Answer 1

The correct option is: (D) 3/8 F 

Explanation:

When one sphere is touched, the charged divides equally (½ Q each). When this sphere is then touched to the second sphere, the net charge (3/2 Q) is divided equally (¾ Q each). Since F ∝ q₁q₂, the original force is proportional to Q² and the new force is then proportional to (½ Q)(¾ Q) = 3/8 Q²