Electromagnetic Induction — Electromagnetism

Electromagnetism / Electromagnetic Induction

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Induction — the rules

Faraday. An EMF appears whenever the flux through a circuit changes: ε = −N·dΦ/dt, with Φ = ∫B·dA. No change, no EMF — a huge steady flux induces nothing.

Lenz. The minus sign: the induced current always opposes the change that made it. Approaching pole → the near coil face repels it; retreating pole → it attracts. This is energy conservation in disguise.

Motional EMF. A rod of length L cutting field lines at speed v: ε = BLv (force on carriers qv×B). Rotating rod: ε = ½BωL².

Inductors. ε = −L·dI/dt, energy U = ½LI², time constant τ = L/R. Just after switching an inductor is an open wire; long after, a plain wire. Charge through a coil: q = ΔΦ/R, however fast the change.

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EM Lab · all topics

§01

Faraday's experiment — wave the magnet, read the meter

Drag the magnet through the coil (or let it auto-sweep) and watch the two graphs write themselves: the flux Φ swells as the magnet nears, and the EMF ε = −dΦ/dt spikes only while Φ is changing — fast pass, tall spike; park the magnet anywhere and ε collapses to zero. The needle kicks one way going in, the other coming out, exactly as Lenz demands: the coil always fights the change.

DRAG THE MAGNET THROUGH THE COIL

tip: a fast flick spikes ε; a slow glide barely wakes it

ε = −N dΦdt

flux Φ

0 mWb

EMF ε

0 mV

flux steady — no EMF. Move the magnet, or hit auto-sweep.

Lenz = energy conservation

If the coil helped the magnet instead of fighting it, the magnet would accelerate for free and the current would grow forever — a perpetual-motion machine. The minus sign is physics collecting its bill: the electrical energy comes from your push.

LENZ'S LAW · THE COIL BECOMES A MAGNET THAT FIGHTS YOU

green = coil repels · purple = coil attracts

What Lenz's law is saying

Magnet's N pushes in → the coil's near face becomes N and shoves back. Like poles repel: the coil fights the approach.

The two-step trick

1. Which way is the flux changing? 2. The induced current flows so its own field opposes that change — propping up a falling flux, blocking a rising one. That is the whole minus sign.