Question

The rotor in a certain electric motor is a flat, rectangular coil with 89 turns of wire and dimensions 2.57 cm by 4.20 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 3.72 103 rev/min.

(a) Find the maximum torque acting on the rotor.
0.000815N

Answer 1

The rotor in a certain electric motor is a flat, rectangular coil with 85 turns of wire and dimensions 2.25 cm by 4.36 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 10.9 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 3.63 10³ rev/min.

(c) Determine the amount of work performed by the magnetic field on the rotor in every full revolution.
___________________J

(d) What is the average power of the motor?

Potential energy of a coil in a magnetic field is given by

U = N I A B = 85 * 0.0109 * 0.0225 * 0.0436 * 0.8 = 0.000727 Joules

the work done in half a cycle is twice this or 0.001454 Joules

work done in a full revolution is twice this value, or

0.001454 * 2 = 0.002908 Joules

(b) average power of the motor is the work done divided by the time for one rotation.

time = 60 seconds / 3630 rotations = 0.01653 seconds for one rotation so

avg power = 0.002908 J / 0.01653 s = 0.176 Watts