question_answer

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 mid-point of A and B. Find the magnitude of force on C.

A)  F/2                                       

B)  F/8

C)  F           

D)         Zero

Correct Answer: C

Solution :

From Coulombs law, the force of attraction between two charged particles\[(q)\], kept at distance r apart is when two identical spheres are brought in contact, charge on them is equalized, hence total charge on\[C\]is equally shared when brought in contact with sphere\[B\]having a charge\[q\]. Therefore, charge on\[B\]and\[C\]is\[\frac{q}{2}\] . From Coulombs law, the force on\[C\]is \[{{F}_{C}}=\frac{q\times q/2}{4\pi {{\varepsilon }_{0}}{{(r/2)}^{2}}}-\frac{(q/2)(q/2)}{4\pi {{\varepsilon }_{0}}{{(r/2)}^{2}}}\]       \[=\frac{qq}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}(2-1)=F\] Note: The force will be opposite because\[A\]and\[B\]spheres will repel the third sphere.