1. Tardigrade
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  3. Physics
  4. A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I=I0 cos (300 t) where I0 is constant. If the magnetic moment of the loop is N μ0 I 0 sin (300 t ), then ° N ' is

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Q. A long circular tube of length $10\, m$ and radius $0.3\, m$ carries a current I along its curved surface as shown. A wire-loop of resistance $0.005$ ohm and of radius $0.1\, m$ is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $I=I_{0} \cos (300\, t)$ where $I_{0}$ is constant. If the magnetic moment of the loop is $N \mu_{0} I _{0} \sin (300\, t )$, then $^{\circ} N '$ isPhysics Question Image

JEE AdvancedJEE Advanced 2011

Solution:

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