The rotor in a certain electric motor is a flat, rectangular coil with 87 turns

Question

The rotor in a certain electric motor is a flat, rectangular coil with 87 turns of wire and dimensions 2.33 cm by 3.88 cm. The rotor rotates in a uniform magnetic field of 0.800 T. When the plane of the rotor is perpendicular to the direction of the magnetic field, the rotor carries a current of 10.6 mA. In this orientation, the magnetic moment of the rotor is directed opposite the magnetic field. The rotor then turns through one-half revolution. This process is repeated to cause the rotor to turn steadily at an angular speed of 3.36 times 103 rev/min. Find the maximum torque acting on the rotor. Find the peak power output of the motor. Determine the amount of work performed by the magnetic field on the rotor in every full revolution. What is the average power of the motor?

Explanation / Answer

Area

A=0.0233*0.0388 =9.04*10^-4 m^2

a)

Maximum torque

Tmax =NIABsin90 =87*(10.6*10^-3)*(9.04*10^-4)*0.8*1

Tmax=6.67*10^-4 N-m

b)

W=3.36*10^3*(2pi/60)

W=351.86 rad/s

Pmax =Tmax*W=6.67*10^-4*351.86

Pmax=0.2347 W

c)

for 1/2 revolution

W=Umax-Umin=2Tmax =2*6.67*10^-4

W=1.334*10^-3 J

d)

Pav=W/t =1.334*10^-3/(60/3600)

Pav=0.08 W

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