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Q.

Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is 

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a

F

b

3F / 4

c

F / 2

d

F / 4

answer is A.

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Detailed Solution

Initially 

Question Image

F=kQ2r2      …….(i)

Finally 

Question Image

Force on C due to A, FA=k(Q/2)2(r/2)2=kQ2r2

Force on C due to B, FB=KQ(Q/2)(r/2)2=2KQ2r2

∴Net force on C, Fnet =FB−FA=kQ2r2=F

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