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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 :- |
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Answer» 0.5 rad/sec `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` |
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