Electromagnetic Induction: Faraday's Law Simulator

simulator beginner ~8 min
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EMF ≈ 0.63 V peak — from a 10-turn coil rotating at 2 Hz in a 0.5 T field

A coil with 10 turns and 0.01 m² area rotating at 2 Hz in a 0.5 T magnetic field generates a peak EMF of about 0.63 volts. The EMF varies sinusoidally as the flux through the coil changes during rotation, demonstrating Faraday's law of induction.

Formula

ε = -NdΦ/dt (Faraday's law)
Φ = BAcos(ωt) (flux through rotating coil)
ε_peak = NBAω (peak EMF for generator)

Faraday's Discovery: Electricity from Magnetism

In 1831, Michael Faraday made one of the most important discoveries in physics: a changing magnetic field induces an electric current. By moving a magnet through a coil of wire, he generated electricity without any battery. This principle — electromagnetic induction — is the foundation of virtually all electrical power generation in the world today.

The Law of Induction

Faraday's law is elegantly simple: the induced EMF equals the negative rate of change of magnetic flux. For a rotating coil in a uniform field, the flux varies as Φ = BAcos(ωt), and the induced EMF is ε = NBAω sin(ωt). The EMF is maximum when the flux is changing fastest (coil perpendicular to field) and zero when the flux is at its peak (coil parallel to field).

Lenz's Law and Energy Conservation

The negative sign in Faraday's law reflects Lenz's law: the induced current always opposes the change that produced it. If the flux is increasing, the induced current creates a field that resists the increase. This opposition is not merely a mathematical sign — it requires mechanical work to maintain the changing flux, which is how generators convert mechanical to electrical energy.

From Faraday to the Power Grid

Every power plant in the world — whether coal, nuclear, hydro, wind, or gas — generates electricity using Faraday's law. Turbines spin coils in magnetic fields (or magnets past coils), producing alternating current at 50 or 60 Hz. The voltage is then stepped up by transformers (also based on induction) for efficient long-distance transmission.

FAQ

What is Faraday's law of induction?

Faraday's law states that a changing magnetic flux through a loop induces an electromotive force (EMF): ε = -NdΦ/dt. The EMF is proportional to the rate of change of flux and the number of turns. This is the principle behind all electric generators.

What is magnetic flux?

Magnetic flux (Φ) is the total magnetic field passing through a surface: Φ = BAcos(θ), where B is the field strength, A is the area, and θ is the angle between the field and the surface normal. Flux changes when any of these quantities change.

What is Lenz's law?

Lenz's law states that the induced current flows in a direction that opposes the change in flux that caused it. This is the negative sign in Faraday's law. It ensures energy conservation — you must do work to change the flux.

How does a generator work?

A generator rotates a coil (or magnet) to continuously change the magnetic flux through the coil. This changing flux induces an alternating EMF (and current) according to Faraday's law. The mechanical energy of rotation is converted to electrical energy.

Sources

Embed

<iframe src="https://homo-deus.com/lab/electromagnetism/electromagnetic-induction/embed" width="100%" height="400" frameborder="0"></iframe>
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