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 :
A. `(1000)t^(2)`tesla
B. `(2000)^(2)` tesla
C. `(500)^(2)` tesla
D. `(1000)t` tesla