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Therefore, emf is expressed as = (+) where is emf and v is the unit charge velocity. In a macroscopic view, for charges on a segment of the loop, v consists of two components in average; one is the velocity of the charge along the segment v t , and the other is the velocity of the segment v l (the loop is deformed or moved).
Generating an emf through a variation of the magnetic flux through the surface of a wire loop can be achieved in several ways: the magnetic field B changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger), the wire loop is deformed and the surface Σ changes,
This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called back EMF. Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. [1]
where is the EMF and Φ B is the magnetic flux through a loop of wire. The direction of the electromotive force is given by Lenz's law. An often overlooked fact is that Faraday's law is based on the total derivative, not the partial derivative, of the magnetic flux. [1]
In electromagnetism, an eddy current (also called Foucault's current) is a loop of electric current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnetic field. Eddy currents flow in closed loops within conductors, in planes ...
Given a loop of wire in a magnetic field, Faraday's law of induction states the induced electromotive force (EMF) in the wire is: = where = (,) is the magnetic flux through the loop, B is the magnetic field, Σ(t) is a surface bounded by the closed contour ∂Σ(t), at time t, dA is an infinitesimal vector area element of Σ(t) (magnitude is ...
In integral form, it states that the work per unit charge required to move a charge around a closed loop equals the rate of change of the magnetic flux through the enclosed surface. The electromagnetic induction is the operating principle behind many electric generators : for example, a rotating bar magnet creates a changing magnetic field and ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.