The electromagnetic induction is generating voltage by varying the magnetic flux passing through a circuit.
For years, scientists tried to generate electricity by bringing magnets close to wires. They always failed. A powerful magnet stuck to a coil generates nothing. The voltmeter reads absolute zero.
In 1831, Faraday noticed something subtle: the voltmeter needle did not move while the magnet was still, but it did give a small jump exactly at the instant he moved the magnet.
He discovered the key: What generates electricity is not the magnetic field itself, but the change in the magnetic field.
Faraday’s Law: The Derivative of Flux
Faraday formalized that the induced Electromotive Force (𝜀) (the generated voltage) is proportional to the rate at which the magnetic flux through the circuit changes.
Mathematically, it is the time derivative of the Magnetic Flux (𝛷):
Where:
- 𝜀: Induced voltage (Volts).
- 𝑁: Number of turns in the coil (more turns = more voltage).
- 𝑑𝛷 / 𝑑𝑡 : Change in magnetic flux over time (Webers/second).
Physical Interpretation
To generate electricity, you must vary the number of magnetic lines crossing the coil. You have three ways to do this:
- Move the magnet: Bring it closer or farther away quickly (you change 𝐵).
- Move the coil: Rotate it within the field (you change the angle 𝜃, this is how generators work).
- Change the source current: If the field comes from an electromagnet, turn it on and off (you change 𝐵 without moving anything, this is how transformers work).
If 𝛷 is constant ⇒ Derivative is 0 ⇒ Voltage is 0.
Lenz’s Law: The “Minus” Sign
Notice the negative sign in the previous formula. It is not a mathematical decoration. It is a fundamental law of nature discovered by Heinrich Lenz.
Lenz’s Law states:
“The induced current always flows in a direction such that it opposes the cause that produces it.”
It is the principle of Electromagnetic Inertia. Nature hates changes in magnetic flux and fights to keep them constant.
Why Is It Necessary? (Conservation of Energy)
If Lenz’s Law were reversed (positive sign), bringing the magnet closer would cause the coil to attract it more, which would generate more current, which would attract the magnet even more…
The magnet would accelerate infinitely without any external energy input. We would have created energy from nothing.
The negative sign is what guarantees thermodynamics is fulfilled: to extract electricity, you must pay with mechanical force (“magnetic braking”).
Real-World Applications
The Electric Generator
We rotate a coil within a constant magnetic field. The flux passing through it varies sinusoidally (maximum, zero, negative…).
Deriving the cosine, we obtain a sine.
You have just generated Alternating Current.
The Magnetic Brake
In trucks and trains, to brake without wearing out pads, we induce currents in metal discs (Eddy Currents). According to Lenz, these currents create magnetic fields that oppose the wheel’s rotation, gently slowing the vehicle.
Induction Cooktops
The coil under the glass creates a magnetic field that varies 20,000 times per second. The bottom of the pan (ferromagnetic) tries to oppose this drastic change by creating massive internal currents that heat the metal through the Joule effect.
