Question

A point charge $q_1$ exerts an electric force on a second point charge $q_2$. If a third charge $q_3$ is brought near to $q_2$, the electrostatic force exerted by $q_1$ on $q_2$ will
(Presence of charges in the vicinity does not change the force between any two charges)

• A. decrease
• B. increase
• C. remain unchanged
• D. increases, if $q_3$ is of same sign as $q_1$ and decreases, if $q_3$ is of opposite sign.

Answer 1

The correct option is C remain unchanged

According to superposition principle, net force on $q_2$ is,
${\overrightarrow{F}}_{\text{net}}={\overrightarrow{F}}_{21}+{\overrightarrow{F}}_{23}$
${\overrightarrow{F}}_{21}$ is force on $q_2$ due to $q_1$
${\overrightarrow{F}}_{23}$ is force on $q_2$ due to $q_3$

$\Rightarrow$ As there is no change in relative positions of $q_1\&q_2,$ the electrostatic force on $q_2$ due to $q_1$ will not change.
$\because |{\overrightarrow{F}}_{21}|=\frac{k{q}_1{q}_2}{r^2}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Caution: Always remember force exerted by one charge on}\\ \text{another one is independent of the presence of a nearby charge.}\\ \text{Although}{\overrightarrow{F}}_{\text{net}}\text{will take into account the vector sum of all interacting forces.}\end{array}$