question_answer 17)

The line charge  per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Figure). A uniform magnetic field extends over a circular magnetic field extends over a circular region within the rim. It given by                                                      = 0                                          [otherwise]                 What is the angular velocity of the wheel after the field is suddenly switched off?  

Answer:

in magnetic field is given by,                                 The work done in moving the charge once around the loop due to electric field E produced by the magnetic field is given by                                                                                        ?? (i)                 But, from Faraday?s law of electromagnetic induction,                                                                     ?. (ii)                 Equating (i) and (ii),                                 Multiplying both sides by q dt and rearranging, we get                                     ?? (iii)                 But Impulse= Change in momentum of the wheel.                                 from eqn. (iii),                                 But and(in magnitude)                 or                 In vector form,