Motors

Conversion of electrical energy into mechanical torque via the Laplace force.

Conceptual context

An electric motor is a device that converts electrical energy into rotational mechanical energy. It is the functional inverse of the generator: whereas the generator moves a conductor through a field to induce a voltage, the motor feeds a conductor with current so that the field imposes a movement on it. This inversion is not coincidental; both phenomena are manifestations of the same principle of interaction between moving charges and magnetic fields, and they share the same underlying equations.

Motors are the most widespread machine in modern civilisation. They drive everything from electric car windows to high-speed trains, including compressors in air-conditioning units, hard drives and hospital pumps. Understanding their operation at a physical level is not an academic exercise: it is understanding why certain design decisions have inevitable energetic and mechanical consequences.

🟢 Essential level

An electric motor converts electrical energy into rotation through the force exerted by a magnetic field on a current-carrying conductor. That force, perpendicular to both conductor and field, produces rotational torque when the conductor is attached to a mechanical shaft. The rotation direction depends on the current direction: reversing the current reverses the rotation direction.

The motor is conceptually a generator operating in reverse. While the generator produces electricity by rotating, the motor consumes electricity to rotate. Both devices share the same physical structure: a conductor moving inside a magnetic field. The difference is the energy source that drives the process.

This symmetry between motor and generator reveals a profound property of nature: electricity and motion are intimately related. The same device can function as a motor or as a generator depending on how it is energized. A hybrid car's electric drive exploits exactly this duality, acting as a motor to accelerate and as a generator to recharge the battery while braking.

🔵 Formal level

Basic formulas

The mathematical description begins with the Laplace force on a conductor. A conductor of length $L_c$ carrying current $I$ inside a field $B$ experiences a force proportional to the product of these magnitudes and the sine of the angle. With $N_c$ active conductors, the total force is:

Laplace force on the active conductor

This force acts tangentially at distance $r_a$ from the axis, generating motor torque $\tau_m$ that overcomes the load resistance:

Torque of the electric motor

Real student questions

Why does the motor draw more current when it is stopped than when it is running? Because at rest back-EMF is zero and the full voltage drops across the small internal resistance. While running, $\varepsilon_c$ grows and reduces the voltage difference available to drive the current.

Why does reversing the supply polarity reverse the direction of rotation? Because it reverses the direction of $I$, which reverses the direction of the Laplace force according to the right-hand rule.

Can a motor act as a generator? Yes. If an external force rotates the shaft faster than what corresponds to the supply voltage, $\varepsilon_c$ exceeds the supply and current reverses: the motor returns energy to the supply. This phenomenon is called regenerative braking.

Why do motors heat up more under heavy load? Because heavy load demands more torque, torque demands more current, and Joule losses are proportional to the square of the current.

Final synthesis

The electric motor converts electrical energy into mechanical torque through the force that the stator field exerts on the rotor current. Torque is proportional to current, field and the motor's constructive parameters. $\varepsilon_c$, generated by the same rotor as it rotates, limits current at steady state and is the mechanism by which energy is transferred to the shaft. Efficiency measures the quality of that conversion and is always less than one due to unavoidable losses. The motor's operating point is the intersection of its torque-speed curve and the resistive torque curve of the load.