Question

Three charge $q,Q,4q$ are placed in a straight line of length $l$ at points distant $0,\frac{l}{2},l$ respectively from one end. In order to make the net force on $q$ zero, the charge $Q$ must be equal to :

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

Answer 1

The correct option is A $-q$

${\left(F_{net}\right)}_q=0\Rightarrow k\frac{Qq}{{\left(\frac{l}{2}\right)}^2}+k\frac{4q^2}{l^2}=0$
Where $k=\frac{1}{4\pi {\epsilon }_0}$

$\Rightarrow 4Qq+4q^2=0\Rightarrow Q=-q$