Question

Two point charges of charge values Q and q are placed at a distance of $x$ and $x/2$ respectively from a third charge of charge value $4q$, all charges being in the same straight line. Calculate the magnitude and nature of charge Q, such that the net force experienced by the charge q is zero. (Assume q is located between charges $4q$ and Q)

Answer 1

$\text{Step 1: Draw the figure}$

Considering all charge to be positive in the beginning, mention the direction of forces.

$\text{Step 2: Net force on charge q}$

Net force on $q=0$ (Given)

$\Rightarrow F_Q-F_{4q}=0$

(Use Coulomb's law to calculate force experienced by charge $q$ due to other charges)

$\Rightarrow \frac{1}{4\pi {ϵ}_0}\frac{q\times Q}{(x/2{)}^2}=\frac{1}{4\pi {ϵ}_0}\frac{4q\times q}{(x/2{)}^2}$

$\Rightarrow Q=4q$

Hence the magnitude of charge $Q$ should be $4q$ in order to make the total force on $q$ to be zero. and it is positive in nature.