Two positive point charges $q_1=16\mu C$ and $q_2=4\mu C$, are separated in vacuum by a distance of $3.0m$. Find the point on the line between the charges where the net electric field is zero.

Between the charges, the contributions of the two fields have opposite directions, and the net electric field is zero at a point (say $P$) where the magnitudes of $E_1$ and $E_2$ are equal. However, since $q_2<q_1$, point  $P$ must be closer to $q_2$, in order that the field of the smaller charge can balance the field of the larger charge.

At $P,E_1=E_2$

or  $\frac{1}{4\pi {\epsilon }_0}\frac{q_1}{r_1^2}=\frac{1}{4\pi {\epsilon }_0}·\frac{q_2}{r_2^2}$

 $\therefore \frac{r_1}{r_2}=\sqrt{\frac{q_1}{q_2}}\approx \sqrt{\frac{16}{4}}=2$             ……(i)

Also,  $r_1+r_2=3.0 m$                           ……(ii)

Solving these equations, we get

 $r_1=2m$ and $r_2=1m$

Thus, the point $P$ is at a distance of $2m$ from $q_1$ and $1m$ from $q_2$.