Question

Three charge +4q, Q and q are placed in a straight line of length $l$ at points distance 0, $\frac{l}{2}$ and $l$ 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. $-q/2$
• D. $4q$

Answer 1

The correct option is A $-q$

Two force are acting on $q$ one due to $4q$ and second due to $Q$

$F_1=\frac{1}{4\pi {ϵ}_0}\frac{4q^2}{12}{F}_2=\frac{1}{4\pi {ϵ}_0}\frac{Qq}{(1/2{)}^2}=\frac{1}{4\pi {ϵ}_0}\frac{\left(4Q\right)q}{12}{F}_1+F_2=0\frac{1}{4\pi {ϵ}_0}\frac{\left(4q\right)q}{12}+\frac{1}{4\pi {ϵ}_0}\frac{\left(4Q\right)q}{12}=0Q=-q$