Electromagnetic induction

Electromagnetic induction, or magnetic induction, happens when a changing magnetic field creates an electromotive force (emf) across an electrical conductor. The discovery is generally credited to Michael Faraday in 1831, and James Clerk Maxwell later gave it a mathematical description known as Faraday's law of induction. Lenz's law determines the direction of the induced field. Faraday's law was eventually broadened into the Maxwell–Faraday equation, one of the four Maxwell equations that form the foundation of his theory of electromagnetism. This phenomenon is used in many applications, including electrical components like inductors and transformers, and devices such as electric motors and generators.

Michael Faraday published his discovery of electromagnetic induction in 1831, and Joseph Henry independently found it the following year. In Faraday's first demonstration, on August 29, 1831, he wrapped two wires on opposite sides of an iron ring, similar to a modern toroidal transformer. Expecting a wave-like effect from his knowledge of electromagnets, he connected one wire to a galvanometer and the other to a battery. When he made or broke the battery connection, he saw a brief current—which he called a "wave of electricity"—caused by the change in magnetic flux. Within two months, Faraday found other examples: sliding a bar magnet quickly in and out of a wire coil produced transient currents, and rotating a copper disk near a bar magnet with a sliding contact generated a steady direct current (Faraday's disk). He explained induction using his concept of lines of force, but most scientists rejected his ideas because they lacked mathematical form. James Clerk Maxwell was an exception, using Faraday's ideas to build his quantitative electromagnetic theory. In Maxwell's model, the time-varying aspect of induction appears as a differential equation; Oliver Heaviside later called this Faraday's law, though it differs slightly from Faraday's original version and excludes motional emf. Heaviside's form, now known as the Maxwell–Faraday equation, is the one included in Maxwell's equations. In 1834, Heinrich Lenz formulated his law to describe the flux through a circuit, giving the direction of the induced emf and current.

Faraday's law of induction uses magnetic flux (ΦB), defined by a surface integral: ΦB = ∫Σ B · dA, where dA is a surface element, B is the magnetic field, and the dot product represents an infinitesimal amount of flux. Visually, the flux through a wire loop is proportional to the number of magnetic field lines passing through it. When this flux changes, the loop gains an emf. The common version of the law states that the induced emf in any closed circuit equals the negative rate of change of the magnetic flux through it: ℰ = –dΦB/dt. Lenz's law gives the direction: the induced current opposes the change that produced it, which is why the equation has a negative sign. To increase the emf, one can use a tightly wound coil of N identical turns, each with the same flux, producing an emf N times that of a single wire: ℰ = –N dΦB/dt. An emf can be generated by varying the magnetic flux through a wire loop in several ways, such as changing the magnetic field B (for example, with an alternating field) or moving the loop relative to a magnet.