Question

A cylindrical cavity of diameter a exists inside a cylinder of diameter $2a$ as shown in the figure. Both the cylinder and the cavity are infinity long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12}{\mu }_{0}aJ$, then the value of $N$ is

Answer 1

Answer: 5

$B=\frac{{\mu }_0\left(J\pi a^2\right)}{2\pi a}-\frac{{\mu }_0\left(J\pi a^2/4\right)}{2\pi \left(\frac{3a}{2}\right)}$
$B=\frac{5{\mu }_{0}Ja}{12}=\frac{{\mu }_{0}NJa}{12}$
So $N=5$