Question

Two point charges $+8\, \mu \,C$ and $+12 \,\mu \,C$ repel each other with a force of $48 \,N$. 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 $F_{1}=48 \,N$
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} =2 \,N $