A and B are two identical spherical charged bodies which repel each . . .

Question : A and B are two identical spherical charged bodies which repel each other with force F, kept at a finite distance. A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at midpoint of A and B. Find the magnitude of force on C.


Doubt by Tushar

Solution :

q1=q2=q 

Case I : When there are just two charges then 
according to Coulomb's Law the force of repulsion between them
F=kq1q2/r2
F=kq2/r2

Case II : When the third uncharged sphere is touched with B and then placed in between the two. 

q1'=q
q2'=q/2
q3'=q/2
r'=r/2

Force on Sphere C due to A
FCA = kq3'q1'/(r/2)2
FCA = k(q/2)(q)/(r/2)2
FCA = 2kq2/r2 (Towards B)

Force on Sphere C due to B
FCB = kq3'q2'/(r/2)2
FCB = k(q/2)(q/2)/(r/2)2
FCB = kq2/r2 (Towards A)

Net Force of Sphere C

F' = FCA-FCB
F' = 2kq2/r2 - kq2/r2
F' = kq2/r2 (Towards B)
F' = F (Towards B) 
Magnitude of Force on C is equal to magnitude of force between A and B.