Electric Motors: Exploring Torque, Magnetic Fields, and Energy Conversion

What Are Electric Motors?

Electric motors convert electrical energy into mechanical energy using the interaction between magnetic fields and current-carrying conductors.

Key Concepts in Electric Motors

Magnetic Force on a Current-Carrying Wire

The force on a wire in a magnetic field is given by:
\[
F = BIL \sin\theta
\]
Where:

• \(B\): Magnetic field strength (T, Tesla)
• \(I\): Current (A, Amperes)
• \(L\): Length of wire in the field (m)
• \(\theta\): Angle between \(B\) and \(I\)

Torque (\(\tau\)) in Motors

The rotational force in a motor coil:
\[
\tau = BIA N \sin\theta
\]
Where:

• \(A\): Area of the loop (m²)
• \(N\): Number of turns in the coil
• \(\theta\): Angle between field and coil normal

Applications of Electric Motors

Transportation

• Electric vehicles (torque: 200-500 N·m typical)
• High-speed trains (power: 5-10 MW per motor)

Industry

• Conveyor systems (1-50 HP motors)
• Robotic arms (precision servo motors)

Home Appliances

• Washing machines (universal motors)
• Refrigerator compressors (induction motors)

Example Problem

A rectangular loop (\(10 \, \text{cm} \times 5 \, \text{cm}\)) has 100 turns, carries \(3 \, \text{A}\), and is in a \(0.5 \, \text{T}\) field. Find maximum torque.

1. 1. Calculate Area:

\[
A = 0.1 \, \text{m} \times 0.05 \, \text{m} = 0.005 \, \text{m}^2
\]

1. 1. Maximum Torque (\(\theta = 90^\circ\)):

\[
\tau = (0.5)(3)(0.005)(100)\sin 90^\circ = 0.75 \, \text{N·m}
\]

Common Mistakes

1. Using cm instead of m for area calculations
2. Omitting the \(\sin\theta\) term in torque calculations
3. Confusing motor torque (\( \tau = BIA N \)) with linear force (\(F = BIL\))

Practice Questions

1. Calculate torque for a circular loop (\(r = 0.2 \, \text{m}\), \(N = 50\)) with \(2 \, \text{A}\) current in \(0.3 \, \text{T}\) field.
2. Explain how commutators maintain rotation in DC motors.
3. Compare induction vs. synchronous motor applications.