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Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction.
In magnetohydrodynamics, the induction equation is a partial differential equation that relates the magnetic field and velocity of an electrically conductive fluid such as a plasma. It can be derived from Maxwell's equations and Ohm's law, and plays a major role in plasma physics and astrophysics, especially in dynamo theory.
Heaviside's version (see Maxwell–Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations. Lenz's law , formulated by Emil Lenz in 1834, [ 13 ] describes "flux through the circuit", and gives the direction of the induced emf and current resulting from electromagnetic induction (elaborated ...
For example, a nearby conductive surface will exert a drag force on a moving magnet that opposes its motion, due to eddy currents induced in the surface by the moving magnetic field. This effect is employed in eddy current brakes which are used to stop rotating power tools quickly when they are turned off.
This equation also is a direct consequence of the linearity of Maxwell's equations. It is helpful to associate changing electric currents with a build-up or decrease of magnetic field energy. The corresponding energy transfer requires or generates a voltage.
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
These equations are inhomogeneous versions of the wave equation, with the terms on the right side of the equation serving as the source functions for the wave. As with any wave equation, these equations lead to two types of solution: advanced potentials (which are related to the configuration of the sources at future points in time), and ...
"Electromagnetic induction: physics and flashbacks" (PDF) by Giuseppe Giuliani – details of the Lorentz force in Faraday's disc "Homopolar Electric Dynamo" – contains derivation of equation for EMF of a Faraday disc; Don Lancaster's "Tech Musings" column, Feb 1998 – on practical inefficiencies of Faraday disc