Electromagnetic Induction
A changing magnetic flux induces an electromotive force and an electric field, the principle behind generators and transformers.
Definition
Electromagnetic induction is the generation of an electromotive force and circulating electric field by a changing magnetic flux, quantified by Faraday's law, with the induced effects opposing the change according to Lenz's law.
Scope
This topic covers Faraday's law of induction, Lenz's law and the direction of induced effects, motional and transformer electromotive force, self- and mutual inductance, and the energy stored in magnetic fields. It treats induced electric fields as non-conservative and introduces eddy currents, while leaving radiation to later topics.
Core questions
- How does a changing magnetic flux drive a current in a circuit?
- Why do induced currents oppose the change that produces them?
- How are inductance and stored magnetic energy defined?
Key concepts
- magnetic flux
- electromotive force
- Faraday's law
- Lenz's law
- self-inductance
- mutual inductance
- eddy currents
- magnetic energy
Key theories
- Faraday's law of induction
- The electromotive force around a loop equals minus the rate of change of magnetic flux through it; in differential form the curl of the electric field equals minus the time derivative of the magnetic field.
- Lenz's law
- The induced current flows so as to oppose the change in flux that causes it, a consequence of energy conservation that fixes the sign in Faraday's law.
Clinical relevance
Induction is the operating principle of electric generators, transformers, induction motors and cooktops, wireless and inductive charging, and the gradient and radiofrequency coils of magnetic resonance imaging.
History
Faraday discovered electromagnetic induction in 1831, with Joseph Henry observing related effects independently. Lenz stated the directional rule in 1834, and Maxwell incorporated induction into his field equations as the curl law for the electric field.
Key figures
- Michael Faraday
- Joseph Henry
- Heinrich Lenz
Related topics
Seminal works
- maxwell1873
- jackson1998
Frequently asked questions
- What is the difference between motional and transformer EMF?
- Motional EMF arises when a conductor moves through a static magnetic field, while transformer EMF arises from a time-varying field through a stationary circuit; both are unified by Faraday's flux rule.
- Why does Lenz's law involve a minus sign?
- The induced current opposes the change in flux to conserve energy; if it reinforced the change, it would create energy from nothing, so the minus sign in Faraday's law reflects this opposition.