Question

For the given system of charges, where should a third charge $+q$ be placed from negative charge, so that third charge experiences no net force?

• A. $\frac{L}{2}$
• B. $L$
• C. $2L$
• D. $3L$

Answer 1

The correct option is C $2L$

Since, third charge is positive in nature and experiences no net force, so $+q$ charge should be placed on the line joining of given two charges and right side of $-4q$ charge (smaller magnitude charge).

Let $x$ be the distance between $-4q$ and $+q$.
So, Net force on charge $+q=0$

$\therefore |{\overrightarrow{F}}_{31}|=|{\overrightarrow{F}}_{32}|$

$\Rightarrow \frac{k\left(9q\right)\left(q\right)}{(L+x{)}^2}=\frac{k\left(4q\right)\left(q\right)}{x^2}$

$\Rightarrow {\left(\frac{x}{L+x}\right)}^2=\frac{4}{9}$

$\Rightarrow \frac{x}{L+x}=\pm \frac{2}{3}$

$\Rightarrow 2L+2x=\pm 3x$

$\Rightarrow x=2L\text{or}-\frac{2L}{5}$

$\because x=-\frac{2L}{5}$ (Not possible)

$\therefore x=2L$

Hence, option $\left(c\right)$ is the correct answer.