Question

Three charge $+4q,Q$ and $q$ are placed in a straight line of length $\ell$ at points distance $0,\ell /2$ and $\ell$ respectively. What should be the value of $Q$ in order to make the net force on $q$ to be zero?

• A. $-q$
• B. $-2q$
• C. $\frac{-q}{2}$
• D. $4q$

Answer 1

The correct option is A $-q$

Two forces are acting on $q$, one due to $4q$ and second due to $Q$.

$F_1=\frac{1}{4\pi ϵ}\left(4q\right)\frac{q}{l^2}$ and

$F_2=\frac{1}{4\pi ϵ}\left(Q\right)\frac{q}{l^2/4}$

And $F_1+F_2=0$

$\Rightarrow \frac{1}{4\pi ϵ}\left(4q\right)\frac{q}{l^2}+\frac{1}{4\pi ϵ}\left(4Q\right)\frac{q}{l^2}=0$

$\Rightarrow \frac{1}{4\pi ϵ}(\left(4q\right)+\left(4Q\right))\frac{q}{1^2}=0$

$\Rightarrow \frac{1}{\pi ϵ}(\left(q\right)+\left(Q\right))\frac{q}{1^2}=0$

$\therefore Q=-q$