Question

Two point charges $+8\mu C$ and $+12\mu C$ repel each other with a force of $48N$. When an additional charge of $-10\mu C$ is given to each of these charges (the distance between the charges is unaltered) then the new force is

• A. repulsive force of 24 N
• B. attractive force of 24 N
• C. repulsive force of 12 N
• D. attractive force of 2 N

Answer 1

Answer: (D)

Given, $q_1=+8\mu C,q_2=+12\mu C$
and $F_1=48N$
When an amount of charge $-10\mu C$ is added to
both of the charges then, these becomes
$q_1^{\prime }=-2\mu C\text{ and }{q}_2^{\prime }=+2\mu C$
The force between two charges,
$F\propto \left|q_1{q}_2\right|$
$\Rightarrow F_1\propto \left|q_1{q}_2\right|$ and $F_2\propto \left|q_1^1{q}_2^1\right|$
and $\frac{F_1}{F_2}=\frac{q_1{q}_2}{q_1^{\prime }{q}_2^{\prime }}\Rightarrow \frac{48}{F_2}=\frac{8\times 12}{2\times 2}$
$\Rightarrow F_2=2N$