Question

A large metal sheet carries an electric current along its surface . Current par unit length is $\lambda$ . Magnetic field near the metal sheet is :

• A. $\frac{{\mu }_0\lambda }{2}$
• B. $\frac{{\mu }_0\lambda }{2\pi }$
• C. ${\mu }_0\lambda$
• D. $\frac{{\mu }_0}{2\lambda \pi }$

Answer 1

The correct option is A $\frac{{\mu }_0\lambda }{2}$

Given: Current per unit length is $\lambda$

Solution: According to Ampere's circuital law:

$\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}i$

$B\times 2l={\mu }_{0}i$

Note: 2l =because there are 2 surfaces of sheet

Now,$B=\frac{{\mu }_{0}i}{2l}$

$B=\frac{{\mu }_0\lambda }{2}$

Hence the correct option is A