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. $4q$

Answer 1

The correct option is A $-q$

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