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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 .
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.
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 ...
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.
Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor.
Maxwell's equations on a plaque on his statue in Edinburgh. Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.
"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
Using an electroscope to show electrostatic induction. The device has leaves/needle that become charged when introducing a charged rod to it. The leaves bend the leave/needle, and the stronger the static introduced, the more bending occurs. However, the induction effect can also be used to put a net charge on an object.