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 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 300 t , where I₀ is constant. If the magnetic moment of the loop is N ₀ I₀ 300 t , then N is

Step-by-step solution

Take the circular tube as a long solenoid. The wires are closely wound. Magnetic field inside the solenoid is B= ₀ n i Here, n= number of turns per unit length n i= current per unit length In the given problem, aligned & n i= I L B & = ₀ I L aligned Flux passing through the circular coil is =B S= ( ₀ I L ) ( r^2 ) Induced emf, e=- d d t =- ( ₀ r^2 L R ) d I d t Induced current, i= e R =- ( ₀ r^2 L R ) d I d t Magnetic moment i A=i r^2 or M=- ( ₀ ^2 r^4 L R ) d I d t Given, I=I₀ 300 t d I d t =-300 I₀ (300 t) Substi