How changing magnetic fields generate currents and power our homes
Faraday’s law states that an emf is induced in a circuit whenever the magnetic flux through it changes, and the size of the emf equals the rate of change of flux, ε = −dΦ/dt. Lenz’s law gives the direction: the induced current always opposes the change that produced it, which is a consequence of energy conservation. A rod of length l moving at speed v across a field B has a motional emf of Blv.
A coil opposes changes in its own current through self-inductance, with induced emf ε = −L dI/dt. In alternating current, voltage varies as V = V₀ sin ωt and the effective value is Vrms = V₀/√2. In AC circuits, inductors and capacitors have reactances X_L = ωL and X_C = 1/ωC, and an LCR circuit resonates when these are equal. Transformers use mutual induction to change voltage: Vs/Vp = Ns/Np.
Why it matters
Every power station generator, the transformers on electricity poles, induction cooktops, metal detectors and wireless phone chargers work by electromagnetic induction. High-voltage transmission reduces power loss on long lines, and transformers step it down safely for homes. This topic links directly to electromagnetic waves and to the electronics of radio tuning circuits.
Key terms
- Magnetic flux
- The product of magnetic field strength and the area it passes through perpendicularly.
- Lenz’s law
- An induced current flows in a direction that opposes the change in magnetic flux causing it.
- Self-inductance
- The property of a coil by which a change in its own current induces an emf in it.
- RMS value
- The steady value of voltage or current that would produce the same heating effect as the alternating one.