Faraday's Law of Induction is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—in other words, a voltage.

It is the fundamental principle behind transformers, inductors, and many types of electric motors and generators.

The law states that the magnitude of the induced EMF in any closed circuit is equal to the rate of change of the magnetic flux through the circuit.

Simply put: a changing magnetic field creates a voltage.

To understand Faraday's Law, one must first understand magnetic flux. It is a measure of the total number of magnetic field lines passing through a given area.

The formula for magnetic flux is: Φ_B = B * A * cos(θ)

Where:

B: The strength of the magnetic field.

A: The area of the loop or coil.

θ: The angle between the magnetic field lines and the normal (perpendicular) to the loop's surface.

Crucially, Faraday's Law depends on the change in this flux, which can be achieved by changing the magnetic field strength (B), the area of the loop (A), or the orientation of the loop (θ).

The mathematical form of Faraday's Law of Induction is:

ε = -N * (ΔΦ_B / Δt)

Where:

ε (epsilon): The induced electromotive force (EMF) or voltage, in Volts (V).

N: The number of turns in the coil of wire.

ΔΦ_B: The change in magnetic flux.

Δt: The change in time over which the flux changes.

The negative sign in Faraday's formula is a representation of Lenz's Law.

Lenz's Law gives the direction of the induced current. It states that the induced current will flow in a direction that creates its own magnetic field to oppose the change in magnetic flux that created it.

This is a consequence of the conservation of energy. If the induced field enhanced the change, it would create a runaway loop of ever-increasing energy, which is impossible.

Faraday's Law is the principle behind much of our modern electrical technology.

Electric Generators: A generator works by rotating a coil of wire inside a magnetic field. This continuous change in magnetic flux (due to the changing angle) induces a steady alternating current (AC). This is how most of the world's electricity is produced.

Induction Cooktops: An alternating current is passed through a coil under the cooktop, creating a rapidly changing magnetic field. This field induces electric currents (eddy currents) directly in the bottom of the ferromagnetic pot, heating it up through resistance.

Transformers: Transformers use two coils to change AC voltage levels. The changing magnetic field from the primary coil induces a voltage in the secondary coil. The ratio of turns in the coils determines whether the voltage is stepped up or down.

Electric Guitar Pickups: The vibrating steel string of a guitar changes the magnetic flux in a small coil located under the strings, inducing a voltage that is then amplified to produce sound.