Question

Three charges 4q, Q and q are in a straight line in the position of 0, $\frac{l}{2}$ and $l$ respectively. The resultant force on q will be zero, if Q =

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

Answer 1

The correct option is A - q

The force between 4q and q; $F_1=\frac{1}{4\pi {ϵ}_0}.\frac{4q\times q}{l^2}$
The force between Q and q; $F_2=\frac{1}{4\pi {ϵ}_0}.\frac{Q\times q}{{\left(\frac{l}{2}\right)}^2}$
We want $F_1+F_2=0$ or $\frac{4q^2}{l^2}=-\frac{4Qq}{l^2}\Rightarrow Q=-q$