Question

A long circular tube of length $10m$ and radius $0.3m$ carries a current I along its curved surface as shown. A wire-loop of resistance $0.005$ ohm and of radius $0.1m$ is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $I=I_0\cos (300t)$ where $I_0$ is constant. If the magnetic moment of the loop is $N{\mu }_0{I}_0\sin (300t)$, then ${}^{\circ }{N}^{\prime }$ is

Answer 1

Answer: 6

$B_{\text{inside }}={\mu }_{0}ni=\frac{{\mu }_{0}I}{L}$
$\therefore E_{ind}=-\frac{d\varphi }{dt}=-\frac{{\mu }_0\left(\pi r^2\right)}{L}\frac{dI}{dt}$
So magnetic moment $=\left(\frac{E_{\text{ind }}}{R}\right)\pi r^2$
$=6{\mu }_0{I}_0\sin (300t)$
Therefore, $n=6$