How does a motor operate based on Lenz's Law and back electromotive force?

Ampère’s Right-Hand Rule reveals that the flow of electric current produces a magnetic field. Accordingly, when a coil is energized, it forms an N-pole or S-pole magnetic field following the rule, which means electric energy can be converted into magnetic energy.

Newton’s law of motion puts forward a classic physical principle: an object in motion stays in motion, and an object at rest stays at rest. It indicates that all physical substances tend to maintain their existing state. In electrodynamics, the potential energy that maintains the original state of a system is defined as electric potential energy. To change the existing stable state, an external force greater than the original potential energy must be applied to break the balance. Once the balance is broken, the physical state is transformed into a new steady state. For example, a stationary object remains static under inherent electric potential energy; external force pushes it to break the static balance, and uniform motion becomes its new stable state. Further external energy input is still required to change this motion state again.

In simple terms, the two objects maintain a fixed distance through mutual restraint. When one side moves closer, the other generates repulsion to block the approach; when one side moves away, the other generates attraction to pull it back. This tendency to maintain a stable relative distance corresponds to Newton’s law of inertia. Since the interaction relies on the mutual conversion of electric energy and magnetic energy governed by Ampère’s Rule, the induced electromagnetic relationship summarized by the two principles is defined as Lenz’s Law.

One of the most intuitive and interesting experiments demonstrating Lenz’s Law is Arago’s disk experiment, a device that uses a moving magnet to drive an aluminum disk. In the experiment, a magnet cannot attract the aluminum disk at rest because aluminum is non-magnetic. However, when the magnet moves rapidly above the aluminum disk, the disk follows the magnet synchronously as if it were magnetically attracted. The core cause is Lenz’s Law. Although aluminum does not conduct magnetism, it conducts electricity. To maintain the original relative distance when the magnet approaches, eddy currents are induced inside the aluminum disk, generating a corresponding magnetic field.

Driven by the combined attractive and repulsive induced magnetic forces, the aluminum disk follows the magnet’s movement, presenting a phenomenon that the non-magnetic aluminum disk is dragged by the magnet.

The most representative industrial application derived from the principle of Arago’s disk and Lenz’s Law is the induction motor. The name of the induction motor is highly appropriate, as its magnetic field is completely generated by electromagnetic induction. Since electromagnetic induction requires a response time, the motor speed cannot synchronize perfectly with the power supply frequency. This non-synchronous operating characteristic is professionally defined asasynchronism or slip in induction motors.

Lenz’s Law essentially explains the working principle of generators: changes in magnetic field energy induce electric energy that opposes the original magnetic field variation, which is a classic application of the law. Similarly, in permanent magnet motors, when an external force drives the rotor to rotate, measurable voltage and current signals appear on the stator coils, which are defined as back electromotive force (Back-EMF). Specifically, the coil induces electric energy to resist the continuous change of magnetic field caused by the approaching or receding permanent magnet.

To increase the maximum speed of a permanent magnet motor, the magnetic flux of the magnet needs to be reduced. Since Back-EMF counteracts the input driving voltage, reducing the magnitude of Back-EMF (by lowering the magnetic energy variation amplitude) allows the motor to operate at a higher speed. This core principle forms the theoretical basis of field weakening control, which effectively extends the maximum speed range of motors.