1. A conducting rectangular loop of mass 0.60kg, resistance 40 , and 2.0m wide i

Question

1. A conducting rectangular loop of mass 0.60kg, resistance 40 , and 2.0m wide is allowed to fall from rest through a uniform magnetic field 6.0 T which is perpendicular to the plane of the loop. The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field). What is the terminal speed?

2. a circular coil of 35 turns and radius 4.7cm is placed with its plane oriented at 90* to a magnetic field of 0.2 T (aka the coil's area vector is parallel to the field). THe field is now increased at a steady rate, reaching a value of 0.5 T after 8 seconds. What emf is induced in the coil?

Explanation / Answer

The mass of the loop m = 0.6kg the resistance of the loop R = 40 the magnetic field B = 6.0T when the loop is allowed to fall from rest through a uniform magnetic field and it reaches a terminal speed , the net force is zero, so from Newton's law               F - mg = 0 then   F = mg but where the force is due to magnetic field        BiL = mg    (Since the magnetic field and length of the loop is perpendicular )       B (e/R) w = mg but the induced emf e = d(BA) /dt                                  = Bw dl/dt                                  = Bw v here dl/dt = velocity (v)       B (B w v)/R w = mg therefore the terminal velocity        v = mg R/ B^2 w^2           = (0.6)(9.8)(40) / (6.0)^2 (2.0)^2           = 1.63 m/s The number of turns n = 35 the radius of the coil r = 4.7cm the change in magnetic field B = 0.5-0.2 = 0.3T The induced emf e = - d/dt                               = - d(NBA) /dt                              = N(r^2) dB/dt                             = (35)(4.7*10^-2)^2 (0.3/8)                             = 0.0091 V   or 9.1mV              

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