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

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 $=\frac{q+\frac{q}{2}}{2}=\frac{3q}{4}$
Now,
$F^{\prime }=F_2-F_1=\frac{\left(K\frac{3q}{4}-K\frac{q}{2}\right)}{\frac{r^2}{4}}\cdot \frac{3q}{4}$
$=\frac{3K{q}^2}{4r^2}=\frac{3F}{4}$