Question

The rotor in a certain electric motor is a flat, rectangular coil with 80 turns of wire and dimensions 2.50 cm by 4.00 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 10.0 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 3.60×10³ rev/min. (d) What is the average power of the motor?

Answer 1

The average power of the motor is 0.153 Watt

To find the average power, the given values are,

No .of turns of the wire = 80

Dimensions is given as, 2.50 cm by 4.00 cm

Magnetic field = 0.800 T.

current = 10 mA.

Angular speed = 3.60 ×10³ rev/min

What is average power?

Average power is defined as the ratio of total work done by the body to the total time taken by the body.

Average power P avg = W / ΔT Watt

W - Work in One revolution

For first one half revolution,

W = 2 NIAB

   = 2× 80×10×10⁻³×0.0250×0.040×0.800× Sin 90°

   = 2 × 6.4 × 10 ⁻⁴

   = 1.2 × 10⁻³ J

For full revolution,

W = 2 × 1.2 × 10⁻³ J

   = 2.56 × 10⁻³ J

Calculating power,

Time for one revolution is  Δt = 60/3600 = 1/60s

Average power = W / Δt

                          = 2.56 x 10⁻³ / (1/60)

                          = 0.153 Watt.

The average power of the motor is 0.153 Watt.

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