Electromagnetic Induction

Electromagnetic induction is a phenomenon in electromagnetism in which an electromotive force (emf) arises from changing magnetic flux or from a conductor’s motion through a magnetic field. In a closed conducting circuit, the induced emf can drive an electric current. Induction connects electrical and magnetic phenomena and provides the operating principle of generators, transformers, and many sensing devices. Its magnitude depends on how rapidly flux changes, rather than simply on the strength of the field. (openstax.org)

Discovery and experimental basis

Michael Faraday demonstrated electromagnetic induction on August 29, 1831, using two insulated coils wound around an iron ring. Passing current through one coil produced a brief current in the other. The apparatus showed that electrical effects could be transferred between separate circuits through a changing magnetic condition, without a direct conducting connection between their wires. (rigb.org)

Further experiments established that moving a magnet into or out of a coil induced an emf. Reversing the motion or the magnet’s poles reversed its direction; faster movement produced a larger emf. A stationary magnet beside a stationary coil produced no induction when the magnetic field remained unchanged. These observations identified change in magnetic flux—not the mere presence of magnetism—as the central condition. (openstax.org)

Magnetic flux and Faraday’s law

Magnetic flux through an oriented surface $S$ is defined by the integral

Here $\mathbf B$ is the magnetic field, and $d\mathbf A$ points normal to the surface. For a flat surface of area $A$ in a uniform field,

where $\theta$ is the angle between the field and the surface normal. Flux can therefore change through variation in field strength, enclosed area, or orientation. In the International System of Units, magnetic flux is measured in webers and emf in volts. (openstax.org)

Faraday’s law of induction states that the emf around a circuit is

For a coil of $N$ turns, each linked by the same flux,

If different turns have different fluxes, their individual flux linkages must instead be summed. The law determines emf; the resulting current also depends on the circuit’s electrical properties. Thus an emf need not imply a sustained current through a complete conducting circuit. (openstax.org)

The negative sign expresses Lenz’s law: an induced current produces a magnetic effect opposing the flux change responsible for it. It opposes an increase or decrease, not necessarily the original field itself. This direction is consistent with conservation of energy. For example, maintaining the motion of a conducting rod against the induced magnetic force requires mechanical work, which can become electrical energy and resistive heating. (openstax.org)

Induced electric fields and motional emf

For a stationary closed contour, a changing magnetic field produces an electric field satisfying

The left side is a line integral around the contour. This relationship is the integral form of the Maxwell–Faraday equation, one of Maxwell’s equations. The induced field can exist even where there is no wire; a conductor supplies mobile charges through which its effects become observable as current. (openstax.org)

Unlike the field associated with electrostatics, an induced electric field can have nonzero circulation around a closed path. It therefore cannot generally be represented solely by a single-valued electric potential. This distinction explains why induced emf is more general than an ordinary potential difference between two points. (openstax.org)

Motional emf arises when a conductor moves through a magnetic field. The magnetic part of the Lorentz force, $q\mathbf v\times\mathbf B$, acts on its charge carriers and can separate electric charge. For a straight rod of length $\ell$, moving at speed $v$, with the rod, velocity, and uniform field mutually perpendicular,

Both motional induction and induction caused by a changing field can be described through the changing flux of an appropriate circuit. The energy delivered by a mechanically driven conductor comes from the work maintaining its motion. (openstax.org)

Self-induction and stored energy

A changing current also changes the magnetic flux associated with its own circuit. This produces self-induction. For fixed geometry and a linear magnetic response, inductance $L$ relates current to flux linkage, giving

The induced emf opposes changes in current: it does not simply oppose current flow. Inductors exploit this effect in electrical circuits. (openstax.org)

Establishing current in an inductor requires energy to build its magnetic field. For constant $L$, the stored energy is

This energy can return to the circuit as current decreases. Inductance therefore differs from resistance, which dissipates electrical energy rather than reversibly storing it in a magnetic field. (openstax.org)

Technological applications

An electric generator converts mechanical energy into electrical energy by changing flux through conducting windings. In an idealized $N$-turn coil rotating at angular speed $\omega$ in a uniform field,

This produces a sinusoidal emf suitable for alternating current. In an electric motor, rotation can likewise generate a back emf opposing the applied supply voltage. (openstax.org)

An electrical transformer uses changing current in one winding to induce emf in another. Ideally, the voltage ratio equals the turns ratio, $V_s/V_p=N_s/N_p$. Transformers allow voltage changes in an electrical grid without direct electrical contact between the windings; steady direct current does not sustain transformer action. (openstax.org)

Induction also produces eddy currents within bulk conductors. These circulating currents can provide electromagnetic braking and generate heat in induction heating. In transformer and motor cores, unwanted eddy currents cause losses; insulated laminations restrict their paths and reduce those losses. (openstax.org)