The role of changing magnetic flux
Magnetic flux describes the magnetic field through a specified surface and depends on field strength, area and orientation. A changing flux through a closed loop is associated with an induced electromotive force.
Moving a magnet into a coil, changing a coil’s orientation or varying current in another nearby winding can produce induction. Electromotive force and current are distinct: whether current flows, and how large it becomes, also depends on the circuit and its resistance.
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Faraday’s ring-coil experiment
In 1831 Michael Faraday investigated an iron ring carrying two windings at the Royal Institution. Switching current on in one winding produced a temporary response in the second; switching it off produced a response of the opposite direction.
The response disappeared once the first current became steady. The experiment therefore concerned changing magnetic conditions, rather than the mere presence of a current. The preserved apparatus connects the finding to its experimental construction.
Faraday’s law and Lenz’s law
For a fixed single-turn loop, Faraday’s law can be written ε = −dΦB/dt, where ε is the induced electromotive force and ΦB is magnetic flux through a surface bounded by the loop. Faster flux change gives a greater magnitude of induced emf.
The minus sign expresses the direction described by Lenz’s law: the magnetic effect of an induced current opposes the change responsible for it. This is consistent with energy conservation; pushing a magnet to produce current requires work against the electromagnetic response.
Generators and transformers
A generator uses mechanical motion to change flux linked with a coil, converting supplied mechanical energy into electrical energy. A transformer transfers electrical energy through the changing magnetic field associated with current in one winding.
These applications put experimentally established relationships to work in power systems and equipment. Their operation requires an energy input and appropriate circuit conditions; a magnetic field by itself is not an unlimited source of energy.