Question

For the two fixed infinite line charges, the net electric field is zero at a point $\text{P}$ between them. The distance of the point $\text{P}$ from the left infinite line charge is

• A. $1.25\text{m}$
• B. $3.25\text{m}$
• C. $2.25\text{m}$
• D. $0.25\text{m}$

Answer 1

The correct option is A $1.25\text{m}$

Given:
${\lambda }_1=10\text{nC/m};{\lambda }_2=30\text{nC/m}$

Let us suppose, the distance of the point $\text{P}$ from the left infinite line charge is $x$.



And we know, electric field due to an infinite rod is

$E=\frac{2K\lambda }{r}$

From the question, the net electric field at point $\text{P}$ is zero.

$\therefore E_P=0$

$\Rightarrow \frac{2k{\lambda }_1}{x}-\frac{2k{\lambda }_2}{5-x}=0$

$\Rightarrow \frac{10}{x}=\frac{30}{5-x}$

$\Rightarrow 5-x=3x$

$\Rightarrow 4x=5\Rightarrow x=1.25\text{m}$

Therefore, option $\left(b\right)$ is correct.