Question

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be :

• A. $3 F / 2$
• B. $3 F / 4$
• C. $F$
• D. $2 F$

Answer 1

Answer: (B)

When $C$ is placed in contact with $A$, charge on A \& C will be $=\frac{ q }{2}$
Now $C$ is placed in contact with $B$, charge on $B$ $\&$ C will be $=\frac{ q +\frac{ q }{2}}{2}=\frac{3 q }{4}$
Now,
$ F^{\prime}=F_2-F_1=\frac{\left(K \frac{3 q}{4}-K \frac{q}{2}\right)}{\frac{r^2}{4}} \cdot \frac{3 q}{4} $
$ =\frac{3 Kq ^2}{4 r^2}=\frac{3 F}{4}$