Question

Two equally charged identical metal spheres $A$ and $B$ repel each other with a force $3\times 10^{-5}N$. Another identical uncharged sphere $C$ is touched with $A$ and then placed at the midpoint between $A$ and $B$. Net force on $C$ is

• A. $1\times 10^{-5}N$
• B. $2\times 10^{-5}N$
• C. $1.5\times 10^{-5}N$
• D. $3\times 10^{-5}N$

Answer 1

Answer: (D)

Let $q$ be the charge on each metal spheres $A$ and $B$ respectively and $r$ is distance between them, then
$F=\frac{q\times q}{4\pi {\epsilon }_0{r}^2}=3\times 10^{-5}N\dots$(i)
After contact, charge on $C=$ charge on $A=\frac{q}{2}$
Net force on $C=F_{BC}-F_{AC}$
$=\frac{q(q/2)}{4\pi {\epsilon }_0(r/2{)}^2}-\frac{(q/2)(q/2)}{4\pi {\epsilon }_0(r/2{)}^2}$
$=\frac{q^2}{4\pi {\epsilon }_0{r}^2}=3\times 10^{-5}N$ ( Using ( i ))