Question

A hollow cylinder having infinite length and carrying uniform current per unit length $\lambda$ along the circumference as shown in the figure.


Magnetic field inside the cylinder is

• A. $\frac{{\mu }_0\lambda }{2}$
• B. ${\mu }_0\lambda$
• C. $2{\mu }_0\lambda$
• D. None

Answer 1

The correct option is B ${\mu }_0\lambda$

The current in the hollow cylinder is along the circumference. So, it can be visualized as a long solenoid.



Let us consider one small strip of thickness $dl$.

Number of equivalent tuns per unit length is given by,

$n=\frac{1}{dl}$

Using the relation for magnetic field inside solenoid,

$B={\mu }_{0}ni$

$\Rightarrow B=\left({\mu }_0\right)\left(\frac{1}{dl}\right)\left(\lambda dl\right)(\because i=\lambda dl)$

$\therefore B={\mu }_0\lambda$

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