A motor consists of 200 turns of wire with each turn a circular loop of radius 2

Question

A motor consists of 200 turns of wire with each turn a circular loop of radius 25 cm. The maximum magnetic field averaged over a loop is 0.75 T. The resistance of each loop is 0.1 Ohm. If an EMF of 120 V is supplied to the wire what is A) Current through the wire? B) Magnetic moment of the rotating wire loops? C) Peak torque? D) Peak angular acceleration assuming a total effective Inertia of 0.45 kg m^2? E) Assume the loop is in the plane of this page and the angular velocity is directed to the right with the current flowing clockwise at this instant and the magnetic field is directed to the top of the page (zero flux). What is the direction of the induced current? (Sketch picture.) F) At what rotational velocity will the peak induced EMF be equal to the applied EMF?

Explanation / Answer

A)    Current through the wire = 120/(200 * 0.1)   =   6 A

B) Magnetic moment of the rotating wire loops = n * I * A

                                                                         = 200 * 6 * (3.14 * 0.25 * 0.25)

                                                                          = 235.5   A.m2

C)   Peak torque   =   n * I * A * B

                            =   235.5 * 0.75   = 176.625 N.m

D)    Peak angular acceleration =   176.625/0.45    =   392.5   rad/sec2

E)    direction of the induced current =   anticlockwise

F) Here,    BAN * w = 120

=>   0.75 * (3.14 * 0.25 * 0.25) * 200 * w = 120

=> w = 4.076 rad/sec

=>   w   =   0.649 rev/sec          -----------------> rotational velocity

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