Question

Two positive point charges $q_1=8\mu C$ and $q_2=2\mu C$ are separated in vacuum by a distance of $3\text{m}$. Find the point on the line between the charges where the net electric field is zero.

• A. $1$ $\text{m}$ from $8\mu C$
• B. $2$ $\text{m}$ from $8\mu C$
• C. $0.5$ $\text{m}$ from $8\mu C$
• D. $2.5$ $\text{m}$ from $8\mu C$

Answer 1

The correct option is B $2$ $\text{m}$ from $8\mu C$


At point $P$ on the line between the charges, the electric field due to charge $q_1$ will be balanced by the charge $q_2$ such that the net electric field becomes zero.
$E_1=E_2$
$\frac{k{q}_1}{r^2}=\frac{k{q}_2}{(3-r{)}^2}$
$\Rightarrow \frac{(3-r{)}^2}{r^2}=\frac{q_2}{q_1}$
$\Rightarrow \frac{(3-r{)}^2}{r^2}=\frac{2\mu C}{8\mu C}$
$\Rightarrow \frac{3-r}{r}=\pm \frac{1}{2}$
$\Rightarrow 6-2r=\pm r$
$\Rightarrow r=2\text{m},6\text{m}$
As point P is in between charges $\Rightarrow r=2\text{m}$ is correct choice