Math Problem Statement
The rotor in a certain electric motor is a flat, rectangular coil with 78 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, it carries a current of 10.8 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 3600 rev/min.
(a) Find the maximum torque acting on the rotor. 𝜏max = N·m (b) Find the peak power output of the motor. 𝒫max = W (c) Determine the amount of work performed by the magnetic field on the rotor in every full revolution. W = J (d) What is the average power of the motor? 𝒫avg = W
Solution
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Math Problem Analysis
Mathematical Concepts
Electromagnetic Induction
Torque
Power
Rotational Motion
Formulas
Torque: τ = N * I * A * B * sin(θ)
Power: P = τ * ω
Work: W = τ * θ
ω = 2π * f (angular velocity)
Theorems
Maxwell's Equations
Lorentz Force Law
Suitable Grade Level
Grades 11-12
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