Electromagnetic Induction

Electromagnetic induction is the process by which an electromotive force is generated across a conductor when it experiences a changing magnetic field. This principle, first demonstrated by Michael Faraday in 1831 and later described mathematically by James Clerk Maxwell, lies at the heart of modern electrical engineering. Faraday’s observations, alongside Lenz’s explanation of the induced current’s direction, established one of the foundational laws of electromagnetism. The concept was later incorporated into the Maxwell–Faraday equation, one of Maxwell’s four equations, and remains essential to the operation of countless electrical devices.

Historical Development

Michael Faraday’s experiments in 1831 marked the formal discovery of induction. His earliest demonstration involved wrapping two insulated wires around opposite sides of an iron ring. When he connected one wire to a battery, a transient current appeared in the second wire, detectable on a galvanometer. Faraday interpreted this as a wave of electricity, caused not by continuous flow but by the change in magnetic flux when the battery connection was made or broken.
Within weeks, he expanded the range of observed induction phenomena. Sliding a bar magnet in or out of a coil produced momentary currents, and rotating a copper disc near a magnet generated a small but steady direct current. This device, known as Faraday’s disk, became the first recognisable homopolar generator.
Although Faraday explained his results using the idea of “lines of force”, his insights were initially met with scepticism because they lacked a mathematical foundation. Maxwell later adopted and formalised Faraday’s conceptual lines into a quantitative field theory. Oliver Heaviside subsequently expressed the time-varying aspect of Faraday’s findings in the modern form now known as the Maxwell–Faraday equation. Independently, Joseph Henry discovered similar principles in 1832, while Heinrich Lenz formulated a law governing the direction of the induced current in 1834.
Einstein later observed that induction phenomena depend only on the relative motion between conductor and magnet, regardless of which object moves. This symmetry became one of the conceptual paths that contributed to the development of special relativity.

Faraday’s Law and Lenz’s Law

Electromagnetic induction is described through magnetic flux, defined as the surface integral of the magnetic field passing through a loop:

• The magnetic flux is proportional to the number of magnetic field lines crossing a surface bounded by a conductor.
• When this flux changes, an electromotive force is induced around the loop.

Faraday’s law states that the induced electromotive force in a closed circuit equals the time rate of change of magnetic flux passing through it. Mathematically, the emf is given by the negative derivative of the magnetic flux, the negative sign reflecting Lenz’s law. Lenz’s law asserts that the induced current flows in a direction that opposes the change that produced it.
Flux linkage can be greatly increased by forming multiple turns of wire. A coil of N turns yields an induced emf N times greater than that of a single loop under the same flux variation.
Several conditions can produce a change in flux:

• Variation in magnetic field strength, such as that produced by alternating fields.
• Movement of the conductor relative to the field.
• Geometric alteration of the loop, changing its enclosed area.
• Rotation or reorientation of the loop within a fixed magnetic field.
• Any combination of the above factors.

The integral form of the Maxwell–Faraday equation relates the induced emf to the line integral of the electric field around a closed loop. This mathematical description captures the link between changing magnetic fields and induced electric fields, forming a pillar of classical electromagnetic theory.

Motional and Transformer Electromotive Force

Faraday’s law unifies two distinct physical phenomena:

• Motional emf, generated when a conductor physically moves through a magnetic field, causing charges to experience the Lorentz force.
• Transformer emf, produced when a stationary conductor is placed in a region of changing magnetic field, resulting in an induced electric field.

Although the mechanisms differ—one mechanical, one purely electrical—both yield equivalent results and adhere to the same underlying law. This duality has few parallels in physics at such a fundamental level.

Key Applications

Electromagnetic induction underpins a wide range of electrical technologies. Common applications include:

• Transformers, which rely on changing magnetic flux in a primary coil to induce voltage in a secondary coil.
• Inductors, which store energy in magnetic fields and resist changes in current.
• Electric motors, where induced currents contribute to torque generation.
• Electric generators, which convert mechanical motion into electrical power.

Electrical Generators

In generators, mechanical work is used to move conductors through magnetic fields or to change the magnetic flux linking the circuit. This induces an emf that drives current through an external load. Examples include:

• Drum generators, where relative motion between field and coil induces voltage.
• Homopolar generators, such as Faraday’s disk, which produce direct current from a rotating conductive disc in a uniform magnetic field.