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Faraday’s Law of Induction describes how a changing magnetic field creates (induces) an electromotive force (EMF) or voltage in a wire loop. It is the core physical principle behind electric generators, transformers, electrical inductors, and induction cooktops.

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1. Core Concept & Formula

Faraday discovered that voltage is not generated by the simple presence of a magnetic field, but by the change in magnetic flux passing through a circuit over time.

Mathematical Expression:

ε = -N * (ΔΦ / Δt)

• ε = Induced Electromotive Force (EMF) in Volts (V)
• N = Number of turns in the wire coil
• ΔΦ = Change in magnetic flux in Webers (Wb)
• Δt = Change in time in seconds (s)

The negative sign comes from Lenz’s Law, which states that the induced current will always flow in a direction that produces a magnetic field opposing the initial change in magnetic flux.

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2. Visualizing Electromagnetic Induction

When a bar magnet moves relative to a wire coil, the magnetic flux penetrating the loops changes. Moving the magnet faster or adding more turns to the coil increases the total induced voltage.

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3. How Magnetic Flux (Φ) Changes

Magnetic flux is defined as Φ = B * A * cos(θ), where:

• B = Magnetic field strength in Tesla (T)
• A = Surface area of the loop in square meters (m²)
• θ = Angle between field lines and the vector perpendicular to the loop surface

To induce an EMF in a loop, you can change any of these three variables:

1. Change magnetic field strength (B): Move a magnet closer or further away, or modulate an electromagnet.
2. Change loop area (A): Expand, shrink, or squeeze the flexible wire loop inside the magnetic field.
3. Change orientation angle (θ): Rotate the loop inside a fixed magnetic field (the foundational mechanism of AC electric generators).

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4. Key Applications Summary

Application	Mechanism
Electric Generator	Mechanical energy rotates a coil inside a magnetic field to continuously change angle (θ).
Transformer	Alternating current in the primary coil changes magnetic field strength (B) to induce AC in the secondary coil.
Induction Cooktop	Rapidly alternating magnetic fields induce high-frequency eddy currents directly inside cookware metal, producing heat.