Faraday's Law
Faraday's law of induction states that a changing magnetic flux through a circuit induces an electromotive force (EMF) around that circuit, proportional to the rate of change of the flux — the physical principle behind every electric generator, transformer, and induction motor.
Curious
Michael Faraday discovered in 1831 that moving a magnet near (or into) a coil of wire causes a current to flow in the wire — but only while the magnet is actually moving. Hold the magnet perfectly still inside the coil, even right at the centre, and the current vanishes immediately. It's specifically the change in magnetic field passing through the loop that generates the electrical push (EMF), not the field's mere presence.
This single discovery is the foundation of virtually all electricity generation: power plants spin magnets (or coils) to continuously change the magnetic flux through generator windings, converting mechanical motion (from steam turbines, falling water, wind, or other sources) directly into electric current.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| EMF | Induced electromotive force | volt (V) |
| Φ_B | Magnetic flux through the circuit | weber (Wb) |
| t | Time | second (s) |
The negative sign is not a mathematical afterthought — it encodes Lenz's law, which states that the induced current always flows in whichever direction opposes the change in flux that created it. This is a direct consequence of energy conservation: if induced currents instead reinforced the change that created them, the process would runaway and generate energy from nothing, violating the conservation of energy.
Worked example: A circular loop of area 0.05 m² sits in a magnetic field that increases uniformly from 0.2 T to 0.8 T over 0.3 seconds. ΔΦ = ΔB × A = (0.8−0.2)(0.05) = 0.03 Wb. EMF = ΔΦ/Δt = 0.03/0.3 = 0.1 V.
Deep Dive
Faraday's law is one of Maxwell's four equations (see the full Maxwell's Equations page for the complete set of four and the electromagnetic wave derivation). In its local, differential form, ∇×E = −∂B/∂t, it makes a subtler and more general statement than the integral form given above: a time-varying magnetic field, anywhere in space, creates a circulating electric field, whether or not any physical wire or circuit happens to be present to carry a resulting current.
Motional EMF: When a conductor physically moves through a static magnetic field (rather than the field itself changing at a fixed location), the induced EMF can equivalently be derived from the magnetic force on the moving charge carriers within the conductor (F = qv×B) — showing that "motional EMF" and "Faraday's law" are two complementary ways of describing the same underlying physics, connected by the reference-frame-dependent split between electric and magnetic fields discussed in relativistic electrodynamics.
Joseph Henry independently discovered self-induction (and possibly electromagnetic induction itself) at roughly the same time as Faraday, in the early 1830s, working in the United States; historical priority disputes between the two are complicated by publication delays, but Faraday's more complete and widely published experimental account is what became the standard historical reference, and the SI unit of inductance (the henry) is named for Henry in partial recognition of his independent contribution.
Concept Relationship Map
Requires: magnetic field, electric field
Enables: Lenz's law [PENDING FULL ENTRY], inductance [PENDING FULL ENTRY], transformers [PENDING FULL ENTRY], electric generators
Commonly confused with: the false idea that a strong but unchanging magnetic field induces current — only a changing flux does
Sources
- Faraday, M. (1832). Philosophical Transactions of the Royal Society of London, 122, 125–162.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press, Ch. 7.