An ideal solenoid of inductance L = 1H. Radius a = 0.5 m and numbers of turns per unit length is 1000 turns/meter. The solenoid is fixed and empty from inside. A wooden whell is co-axially to the solenoid and it is free to rotate about its axis of symmetry without any friction. The weeden wheel has radius b = 1m, moment of inertia 1 = 1 kg `m^(2)`, about its axis of symmetry and is initially stationary. Charge of `1000 muC` is applied uniformly on the periphery of the wheel. Now the solenoid is connected to a voltage source whose emf varies with time as `epsilon = ((2)/(mu_(0)))`t volt. Now switch is on at t = 0. Neglect the resistance of the solenoid and mutual-inductance between the wheel and solenoid.

Now at t =2, switch is suddenly off. The angular velocity of the wheel after switching off will be :

Options

A. a. zero
B. b. 4 rad/sec
C. c. 2 rad/sec
D. d. 8 rad/sec

Answer

A

Explanation

As the switch is suddenly off, the magnetic field will suddenly become zero. So, an impulsive induced electric field will be generated
`E=(a^(2))/(2b)=((dB)/(dt))`
Impulsive torque will be
`tau = (qE) (b)`
`=(1000xx10^(-6))xx((0.5)^(2))/(2xx1)((dB)/(dt))xx(1)`
`tau=(25)/(2)xx10^(-5)((dB)/(dt))`
Angular impulse `= tau dt = (10^(-3))Delta B = (25)/(2) xx 10^(-5) xx 4000 = 0.5 N-m sec`
`L_(f)=L_(i)+J_(ext)`
`(1)omega_(f)=(1)(0.5)-0.5 =0`.