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

• A. F/2
• B. F/8
• C. F
• D. Zero

Answer 1

Answer: (C)

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 $F_C=\frac{q\times q/2}{4\pi {\epsilon }_0{(r/2)}^2}-\frac{(q/2)(q/2)}{4\pi {\epsilon }_0{(r/2)}^2}$
$=\frac{qq}{4\pi {\epsilon }_0{r}^2}(2-1)=F$
Note: The force will be opposite because $A$ and $B$ spheres will repel the third sphere.