Faraday's law of induction
Faraday's law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. This simply means that the induced emf is proportional to the rate of change of the magnetic flux through a coil.
The relation between the rate of change of the magnetic flux through the surface S enclosed by a contour C and the electric field along the contour:
- <math>\oint_C \mathbf{E} \cdot d\mathbf{l} = - \ { d \over dt } \int_S \mathbf{B} \cdot d\mathbf{A}</math>
where E is the electric field, dl is an infinitesimal element of the contour C and B is the magnetic flux density. The directions of the contour C and of <math>d\mathbf{A}</math> are assumed to be related by the right-hand rule.
Equivalently, the differential form of Faraday's law is
- <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
which is one of the Maxwell equations.
In the case of an inductor coil where the electric wire makes N turns, the formula becomes:
- <math>e=-N{d \Phi \over d t}</math>
where e is the induced electromotive force and dΦ/dt is the time-rate of change of magnetic flux Φ. The direction of the electromotive force (the negative sign in the above formula) was first given by Lenz's law.
Faraday's law, along with the other laws of electromagnetism, was later incorporated into Maxwell's equations, unifying all of electromagnetism.
Faraday's law of induction is based on Michael Faraday's experiments in 1831. The effect was also discovered by Joseph Henry at about the same time, but Faraday published first.[1][2]
See also
- Magnetic flux density
- Ampere's law
- Stokes' theorem
- Vector calculus
- Moving magnet and conductor problem
References
- ^ Ulaby, Fawwaz (2001-01-31). Fundamentals of Applied Electromagnetics, 2nd edition, Prentice Hall, p. 232. ISBN 0-13-032931-2.
- ^ Joseph Henry. Distinguished Members Gallery, National Academy of Sciences. Retrieved on 2006-11-30.
Categories
Electrodynamics | Introductory physics | Eponymous laws