The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of

Question

The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of 1.5 Ohm and a radius of 0.024 m. The magnetic field is directed out of the paper as shown. Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is 3 times in 0.4 s? 0.43 V 0.65 V 0.014 V 0.021 V What is the average current around the loop if the magnitude of the magnetic field is 3 times in 0.4 s? 1.4 times 10-2 A, clockwise 1.8 times 10-2 A, clockwise 1.4 times 10-2 A, counterclockwise 1.8 times 10-2 A, counterclockwise 4.5 times 10-2 A, clockwise

Explanation / Answer

magnetic flux associated with the circular loop is let
= magnetic field * area of loop
   = B *A
   = 3 * * (0.024)2
   = 0.0054 Tm2


magnetic field after 3 seconds = 3B
1 = magnetic field * area of loop
     = 3B *A
     = 3 * 0.0054 Tm2
     
d = 1 -
     = 2 * 0.0054 Tm2
     = 0.0108 Tm2
so answer is e.

(a) induced emf = e = - d/dt
                   = - 0.0108/0.4
                   = - 0.027 volts


(b)   current induced = voltage / resistance
                               = e/r
                               = - 0.027/1.5
                               = - 0.018 Ampere
so current is of magnitude 0.018 A and its direction is counterclockwise
so answer is d.

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