Electromagnetic induction

Electromagnetic induction occurs when changing magnetic flux through a circuit produces an electromotive force (emf). Michael Faraday demonstrated the effect in 1831 by moving magnets and coils relative to one another; a steady magnetic field alone does not induce a current in a stationary closed circuit.¹ Magnetic flux is the field component passing through a specified area, so it can change when the field strength, the area, or the angle between field and surface changes.

Faraday’s law expresses the induced emf as ε = −dΦ_B/dt, or, for a coil of N turns, ε = −N dΦ_B/dt. The minus sign is Lenz’s law: the induced effect opposes the change in flux that produces it. In a closed conducting path, the emf drives an induced current whose magnitude also depends on resistance and the circuit’s inductance.

Induction can arise from a changing field or from motion through a field, although these descriptions are parts of one electromagnetic theory. A stationary loop in a time-varying magnetic field experiences a circulating electric field, while a moving conductor can experience magnetic force on its charges, often called motional emf. In a simple straight conductor moving perpendicularly through a uniform field, the emf is proportional to magnetic-field strength, conductor length, and speed.

Maxwell’s equations generalize Faraday’s result: a changing magnetic field produces a nonconservative electric field whose lines can form closed loops. This distinguishes induction from electrostatic voltage, which is associated with a conservative electric field. The distinction matters in transformers, where no mechanical motion is required, and in generators, where rotation continually changes the flux linked with coils.

Electrical generators convert mechanical work into electrical energy by rotating coils or magnetic fields so that flux changes periodically. Transformers transfer alternating-current energy between circuits through mutual induction, changing voltage and current while operating at essentially the same frequency.¹ Induction motors use related interactions between rotating magnetic fields and currents induced in a rotor.

Practical devices limit unwanted induction as well as exploit it. Transformer cores are laminated to reduce eddy-current losses, and magnetic materials can introduce hysteresis losses. Skin effect causes alternating current to concentrate toward the surface of a conductor at higher frequencies. Induction heating deliberately produces eddy currents in conductive objects, whereas electromagnetic interference can induce unwanted voltages in signal cables, medical equipment, and power systems. Shielding, twisting, grounding, and careful circuit geometry help control these effects.

Induction depends on flux linkage, so geometry can matter as much as field strength. A loop rotating in a uniform field produces an alternating emf even though the field itself is constant; conversely, a changing field may produce little voltage if its net flux through a circuit remains unchanged. Multiple windings also permit mutual induction, while a single coil can oppose changes in its own current through self-inductance.

Faraday’s original experiments included an iron ring with separate primary and secondary coils, an early transformer demonstration, and showed that a transient current in one circuit could induce a transient current in another.² Induction also operates on microscopic scales: magnetic-resonance instruments detect signals from changing magnetic moments, and nondestructive testing uses induced currents to reveal cracks or changes in metal conductivity. The same law therefore links large power networks with precision measurement.

Electromotive force

Energy supplied per unit charge by a source or induced process; it is measured in volts even when no chemical battery is present.

Magnetic flux

The surface integral of magnetic field through an area, measured in webers.

Lenz’s law

The induced current or emf has a direction that opposes the change in magnetic flux producing it.

Mutual induction

Induction in one circuit caused by changing current and magnetic flux associated with another circuit.

Eddy current

A circulating current induced within a bulk conductor by changing magnetic flux.