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Physics
DC motor — Why does the coil turn?
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A single wire loop between magnetic poles. Adjust the current, inspect forces, and compare a split-ring commutator with two slip rings.
N/S magnets, copper loop, shaft, brushes and electrical contacts. Drag the background to rotate the view; use Inspection angle to position the loop with the keyboard.
Preparing the 3D scene…
Simulation pausedSplit-ring commutator
Forward supply
The supply maintains the set current while contact is closed.
N on left · S on right
Changing contacts pauses the model and returns the loop to 45° for comparison.
Setting the angle by hand pauses the model and sets angular velocity to zero.
Calculated by the model
- Rotation
- Stationary
- Torque direction
- Counterclockwise
- Torque about the shaft
- 0.849 mN·m
- Force on each side
- 20.0 mN
- Winding current
- -1.0 A
- θ
- 45.0°
Directions viewed from the +z end of the shaft.
Making contact
The two magnetic forces are equal and opposite, but their lines of action differ. Together they produce torque about the shaft.
Side 1: current inward; side 2: outward
F₁ along −y; F₂ along +y.
Equations and conventions
F = i·l × B; τ = μ × B, where μ = iA·n. The axial sides have |F| = |i|LB; τz = −iAB sinθ, with B signed along +x.
θ measures rotation of the reference normal n about +z from +x; it is not the angle between the loop plane and the field. L = 10 cm, w = 6 cm, A = 60 cm²; one turn.
Forces on the two connecting sides lie along the shaft, with equal and opposite collinear forces. They produce no torque about the shaft.
Model notes
- One rectangular turn in a uniform magnetic field, with a fixed shaft. The connecting sides exert no torque about the shaft; supply leads are outside the ideal field region.
- An ideal regulated DC current source maintains I with closed contacts and switches off at the commutator gaps. Fixed-voltage batteries, back emf, inductance, arcing and iron cores are not simulated.
- Each commutator gap spans 4°. No hidden impulse is added at a dead position; starting at rest in a gap requires repositioning the loop.
- Inertia J = 10⁻⁴ kg·m² and viscous drag b = 1.5×10⁻⁴ N·m·s/rad are illustrative parameters. Rotation is not calibrated to a real motor's rpm, efficiency or design specifications.
- The 0.25× rate slows observation time. Pause freezes the simulation and differs from disconnecting the supply. Arrows and current dots illustrate directions, not force scales or electron speed.