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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:
![\[ F = BIL \sin\theta \]](https://on22.com/wp-content/ql-cache/quicklatex.com-356e0092f4ef997893cd292013ef0ea6_l3.png "Rendered by QuickLaTeX.com")
Where:
![B]( "Rendered by QuickLaTeX.com")
: Magnetic field strength (T, Tesla)![I]( "Rendered by QuickLaTeX.com")
: Current (A, Amperes)![L]( "Rendered by QuickLaTeX.com")
: Length of wire in the field (m)![\theta]( "Rendered by QuickLaTeX.com")
: Angle between ![B]( "Rendered by QuickLaTeX.com")
and ![I]( "Rendered by QuickLaTeX.com")
: Magnetic field strength (T, Tesla)
: 
: 
: Angle between Torque (![\tau]( "Rendered by QuickLaTeX.com")
) in Motors
) in MotorsThe rotational force in a motor coil:
![\[ \tau = BIA N \sin\theta \]](https://on22.com/wp-content/ql-cache/quicklatex.com-2161f9bfa3a7012cf50740d2921b6682_l3.png "Rendered by QuickLaTeX.com")
Where:
![A]( "Rendered by QuickLaTeX.com")
: Area of the loop (m²)![N]( "Rendered by QuickLaTeX.com")
: Number of turns in the coil![\theta]( "Rendered by QuickLaTeX.com")
: Angle between field and coil normal
: Area of the loop (m²)
: Number of turns in the coilApplications 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 (
) has 100 turns, carries 
, and is in a 
field. Find maximum torque.
- Calculate Area:
![\[ A = 0.1 \, \text{m} \times 0.05 \, \text{m} = 0.005 \, \text{m}^2 \]](https://on22.com/wp-content/ql-cache/quicklatex.com-bdf5aa959127b1c09743dae8eb064a4e_l3.png "Rendered by QuickLaTeX.com")
- Maximum Torque (
![\theta = 90^\circ]( "Rendered by QuickLaTeX.com")
):
- Maximum Torque (
): ![\[ \tau = (0.5)(3)(0.005)(100)\sin 90^\circ = 0.75 \, \text{N·m} \]](https://on22.com/wp-content/ql-cache/quicklatex.com-ca4929e36f0087754239785805c6d048_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes
- Using cm instead of m for area calculations
- Omitting the
![\sin\theta]( "Rendered by QuickLaTeX.com")
term in torque calculations - Confusing motor torque (
![\tau = BIA N]( "Rendered by QuickLaTeX.com")
) with linear force (![F = BIL]( "Rendered by QuickLaTeX.com")
)
term in torque calculations
) with linear force (
)Practice Questions
- Calculate torque for a circular loop (
![r = 0.2 \, \text{m}]( "Rendered by QuickLaTeX.com")
, ![N = 50]( "Rendered by QuickLaTeX.com")
) with ![2 \, \text{A}]( "Rendered by QuickLaTeX.com")
current in ![0.3 \, \text{T}]( "Rendered by QuickLaTeX.com")
field. - Explain how commutators maintain rotation in DC motors.
- Compare induction vs. synchronous motor applications.
, 
) with 
current in 
field.
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