Question

Two infinite sheets carrying current per unit length (Surface current density) $10\text{A/m}$ each in opposite directions. What is the magnetic field at point $P$.

• A. $12.56\times {10}^{-5}\text{T}$
• B. $12.56\times {10}^{-7}\text{T}$
• C. $12.56\times {10}^{-6}\text{T}$
• D. $12.56\times {10}^{-8}\text{T}$

Answer 1

The correct option is C $12.56\times {10}^{-6}\text{T}$

Given,

Current per unit length, $\lambda =10\text{A/m}$

Magnetic field at point $P$ for sheet-$1$ is,

${\overrightarrow{B}}_1=\frac{{\mu }_0\lambda }{2}(\to )$

Magnetic field at $P$ due to sheet-$2$

${\overrightarrow{B}}_2=\frac{{\mu }_0\lambda }{2}(\to )$


So, the net magnetic field at point $P$:

${\overrightarrow{B}}_{net}={\overrightarrow{B}}_1+{\overrightarrow{B}}_2=(\frac{{\mu }_0\lambda }{2}+\frac{{\mu }_0\lambda }{2})(\to )$

$\Rightarrow |B_{net}|={\mu }_0\lambda =4\pi \times {10}^{-7}\times 10$

$\therefore |B_{net}|=12.56\times {10}^{-6}\text{T}$

Hence, option (c) is the correct answer.