Electromagnetic Induction & Alternating Current
Syllabus Unit: Electrodynamics
Why it matters
Chapter overview
Electromagnetic induction shows that a changing magnetic flux creates an EMF (Faraday's law) in a direction that always opposes the change producing it (Lenz's law) — the working principle behind generators, transformers, and self and mutual inductance. When the induced or applied EMF alternates, AC circuit theory — impedance, phasors, resonance and power factor — determines how current, voltage and power behave in circuits containing resistors, inductors and capacitors together.
1Faraday's & Lenz's Laws
Faraday's law quantifies the EMF induced by a changing magnetic flux; Lenz's law fixes its direction by demanding that induced effects always oppose the very change producing them.
Learning Objectives
- State Faraday's law of EM induction, EMF = −N dΦ/dt.
- State Lenz's law and explain it as a consequence of the conservation of energy.
- Identify the three ways magnetic flux can change: changing B, changing A, or changing the angle θ.
- Calculate the motional EMF induced in a rod moving through a magnetic field, EMF = Bvl.
Key Terms
Electromagnetic induction was discovered through a subtle but crucial fact: only a **changing** magnetic flux induces an EMF — a steady, unchanging flux, however large, induces nothing at all.
Three ways to change flux
- Change B — moving a magnet toward or away from a coil.
- Change A — a loop's area expanding or shrinking, or a rod sliding on rails.
- Change θ — rotating a coil within a fixed field, the basis of the AC generator.
Lenz's law — the direction
The induced current always opposes the change in flux that caused it: if flux is increasing, the induced current creates a field opposing the increase; if flux is decreasing, it creates a field reinforcing it. This is why work must be done to push a magnet toward a coil — the induced current's own field pushes back. Lenz's law is simply energy conservation in disguise.