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.

Angular velocity of the wheel at t = 2 sec. will be :-

Options

A. a. 0.5 rad/sec
B. b. 1 rad/sec
C. c. 2 rad/sec
D. d. 4 rad/sec

Answer

A

Explanation

As magnetic field is changing induce electric field will be generated
`E_(out)=(a^(2))/(2b)((dB)/(dt))=(250)t`
Torque experienced by the wheel
`tau=(1000xx10^(-6))xx250 txx1=t//4`
`I alpha =(t)/(4)rArr alpha=(t)/(4)`
`(d omega)/(dt)=(t)/(4)rArromega = (t^(2))/(8)`
at `t = 2, omega = (4)/(8) = 0.5 rad//sec`