Question

Two infinite plane sheets $\text{A}$ and $\text{B}$ carrying current in same direction, and current per unit length are $5\text{A/m}$ and $\lambda \text{A/m}$ respectively. Find the value of $\lambda$ so that magnetic field at point $\text{P}$ is zero.

• A. $2.5\text{A/m}$
• B. $10\text{A/m}$
• C. $5\text{A/m}$
• D. $3.33\text{A/m}$

Answer 1

The correct option is C $5\text{A/m}$

The magnetic field at any point, due to an infinite plane sheet, is independent of its distance from the sheet.

So, at the point $\text{P}$, the magnetic field due to sheet $\text{A}$ is,

${\overrightarrow{B}}_A=\frac{{\mu }_0{\lambda }_A}{2}(\to )$

Direction of magnetic field can be obtained with the help of right- hand curl rule.

And due to sheet $B$ is,

${\overrightarrow{B}}_B=\frac{{\mu }_0{\lambda }_B}{2}(\leftarrow )$

Where, ${\lambda }_A$ and ${\lambda }_B$ are the current per unit length of the sheets.

So, the net magnetic field at point $\text{P}$,

$|{\overrightarrow{B}}_{net}|=|{\overrightarrow{B}}_A+{\overrightarrow{B}}_B|=0$ (Given)

$\Rightarrow \frac{{\mu }_0{\lambda }_A}{2}-\frac{{\mu }_0{\lambda }_B}{2}=0$

$\Rightarrow \frac{{\mu }_0{\lambda }_A}{2}=\frac{{\mu }_0{\lambda }_B}{2}$

$\Rightarrow {\lambda }_A={\lambda }_B$

As, ${\lambda }_A=5\text{A/m}$ and ${\lambda }_B=\lambda$

$\therefore \lambda =5\text{A/m}$

Hence, option $\left(C\right)$ is the correct answer.