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.

Magnetic field in the solenoid at time t is :

Options

A. a. `(1000)t^(2)`tesla
B. b. `(2000)^(2)` tesla
C. c. `(500)^(2)` tesla
D. d. `(1000)t` tesla

Answer

A

Explanation

`L=(di)/(dt)=emf=(2)/(mu_(0))t`
`(1) int di=(2)/(mu_(0)) underset(t=0) overset(t=t)(int) t dt rArr i=(1)/(mu_(0))t^(2)`
`B=mu_(0)ni=(mu_(0))(1000)((t^(2))/(mu_(0)))=(1000)t^(2)`