How a DC Motor Works

1. Component Anatomy

The Core Components

A DC motor transforms **electrical energy** into **rotational mechanics**. It relies on the interaction between magnets and electricity.

■ Stator: Permanent magnets providing a constant magnetic field.
■ Rotor: A rotating loop of wire (the armature coil) carrying current.
■ Split-Ring Commutator: A pair of half-rings that rotates with the coil to handle current reversal.

$$\text{Electrical Current} \longrightarrow \text{Rotational Force}$$

Examine the initial layout. Rotate the camera to see the gaps in the brass commutator rings.

2. Magnetic Field

The Magnetic Field ($\mathbf{B}$)

The permanent magnets produce a uniform magnetic flux density, denoted as vector $\mathbf{B}$. By convention, the field lines emerge from the North Pole and enter the South Pole.

This field establishes the coordinate landscape through which current-carrying wires will experience a physical mechanical force.

$$\mathbf{B} = B \, \mathbf{\hat{i}}$$

The glowing vectors represent the horizontal magnetic field pointing left-to-right.

3. Electromagnetism

The Lorentz Force ($\mathbf{F}$)

When current $I$ passes through the loop, a moving charge experiences a magnetic force. The direction of this force on a wire segment of length $\mathbf{L}$ is given by the cross product:

$$\mathbf{F} = I(\mathbf{L} \times \mathbf{B})$$

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Yellow particles show current flow direction. Green arrows show the opposite vertical forces acting on opposite sides of the coil.

4. Rotation Mechanics

Generating Torque ($\boldsymbol{\tau}$)

Because current flows *away* on one side of the coil and *towards* you on the other, the forces act in opposite directions (one UP, one DOWN).

This force couple creates a rotational moment or **Torque** ($\boldsymbol{\tau}$), causing the armature to rotate around its central shaft.

$$\boldsymbol{\tau} = \mathbf{r} \times \mathbf{F}$$

Watch how the forces pull the loop into rotation. This torque drives the physical rotation of the motor.

5. The Engineering Problem

The Stall Point (90°)

At exactly $90^\circ$ (vertical position), the forces pull directly outward and inward. The perpendicular lever arm is zero, causing the torque to drop to zero.

If the current direction remained the same past this point, the forces would reverse the loop's direction, leading to oscillation rather than rotation.

$$\theta = 90^\circ \implies \boldsymbol{\tau} = \mathbf{0}$$

Look closely: At $90^\circ$, the brushes align with the insulating gap in the commutator. Current drops to zero ($I = 0$).

6. The Solution

Split-Ring Action

To maintain continuous rotation, the current in the loop must reverse direction the instant it passes the vertical plane.

The **split-ring commutator** solves this. As the loop rotates past $90^\circ$, each half-ring automatically swaps contact to the opposite brush, reversing the current direction inside the coil so that force remains UP on the left and DOWN on the right!

$$\text{Brush}_1 \leftrightarrow \text{Ring A} \quad \text{Brush}_2 \leftrightarrow \text{Ring B}$$

Observe the loop oscillating around the swap point. Notice current flipping to keep forces pushing the correct way.

7. Sandbox

Continuous Rotation

With the commutator working continuously, the coil experiences constant, unidirectional rotational torque, spinning smoothly.

Motor Speed: 1.0x

Show Field Lines ($\mathbf{B}$) Show Current ($I$) Show Forces ($\mathbf{F}$)

$$\boldsymbol{\tau}_{\text{avg}} > 0 \implies \text{Continuous Work!}$$