Question

Two point charges +4q and +q are placed 30 cm apart. At what point on the line joining them is the electric field is zero?

Answer 1

The electric field will be zero at a point where the forces exerted by charges 4q and q on a test charge $q_0$ are equal and opposite. Let this point be at a distance x from 4q, then its distance from $q=30-x$. If $F_1$ is force due to 4q and $F_2$ due to q, then $F_1=F_2$,
i.e., $\frac{1}{4\pi {ϵ}_0}\frac{4q\times q_0}{x^2}=\frac{1}{4\pi {ϵ}_0}\frac{q\times q_0}{(30-x{)}^2}$
(or) $\frac{4}{x^2}=\frac{1}{(30-x{)}^2}$
$\Rightarrow 2(30-x)=x$
(or) $x=20cm.$