Electromagnetic Induction: Faraday's Law and Lenz's Opposing Current

A moving magnet writes a current

Move a magnet near a coil of wire and, with no battery or wire touching the magnet at all, a current appears in the coil. Michael Faraday demonstrated this in 1831, and the effect is now one of the two or three most economically important discoveries in physics — every generator, transformer and induction motor on Earth runs on it. Faraday's law says the electromotive force (EMF, essentially the induced voltage) around a loop equals the negative rate of change of magnetic flux through it:

ε = -N · dΦ/dt

where Φ is the magnetic flux through one turn of the coil, N is the number of turns, and ε is the induced EMF. Flux itself is Φ = B·A·cos(θ), the magnetic field strength times the area it passes through times the cosine of the angle between the field and the surface normal — which means an induced current can come from a changing field strength, a changing area, or a changing angle; the law only cares about the rate of change of the total flux, not which ingredient is changing.

Lenz's law: nature opposes the change

The minus sign in Faraday's law is not decorative — it is Lenz's law, and it says the induced current always flows in the direction that opposes the change in flux that created it. Push a magnet's north pole toward a coil and the induced current creates its own magnetic field that pushes back against the incoming magnet; pull the magnet away and the induced current instead tries to pull it back. This opposition is not an accident of sign convention, it is a direct consequence of energy conservation — if the induced current instead assisted the change, you could get a magnet accelerating itself and a current growing without bound from nothing, which would violate the first law of thermodynamics.

Why you feel resistance moving a magnet through a coil

Lenz's law is exactly why generating electricity always takes mechanical work: the induced current's opposing magnetic field exerts a real, measurable drag force back on whatever is moving the magnet (or the coil), and that drag is precisely what converts your mechanical push into electrical energy delivered to the circuit. A hand-crank generator feels stiffer the more current it's supplying for exactly this reason — you're not just spinning a shaft, you're fighting an induced field that grows with the load.

The galvanometer as flux detector

A galvanometer needle deflects in proportion to the current flowing through its coil, which makes it a direct, visible readout of Faraday's law: hold the magnet still and the needle sits at zero no matter how strong the field, because dΦ/dt = 0. Move the magnet faster and the needle swings further, because a faster change produces a larger EMF. Reverse the direction of motion and the needle swings the opposite way, a direct demonstration of Lenz's law choosing the current's direction based on whether flux is increasing or decreasing.

From this equation to every generator on the grid

A power-station generator is, in essence, a much larger, continuously-rotating version of the same coil and magnet: a rotor of magnets spins inside (or a coil spins inside a fixed field), continuously changing the flux through the stationary windings and producing an alternating EMF as the angle θ sweeps through a full rotation each cycle — which is exactly why grid power is AC and not DC, and exactly why its frequency (50 or 60 Hz) is set by how fast the rotor physically spins. A transformer uses the same law in a different geometry: an alternating current in one coil creates a changing flux that an adjacent coil, wound with a different number of turns N, picks up as a scaled-up or scaled-down voltage — the ratio of induced voltages is exactly the ratio of turns, which is the entire reason transformers can step voltage up for transmission and back down for household use.

Frequently asked questions

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