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In general, the relation between the emf in a wire loop encircling a surface Σ, and the electric field E in the wire is given by = where dā is an element of contour of the surface Σ, combining this with the definition of flux =, we can write the integral form of the Maxwell–Faraday equation =
The electromotive force generated by motion is often referred to as motional emf. When the change in flux linkage arises from a change in the magnetic field around the stationary conductor, the emf is dynamically induced. The electromotive force generated by a time-varying magnetic field is often referred to as transformer emf.
That is, the back-EMF is also due to inductance and Faraday's law, but occurs even when the motor current is not changing, and arises from the geometric considerations of an armature spinning in a magnetic field. This voltage is in series with and opposes the original applied voltage and is called "back-electromotive force" (by Lenz's law).
Faraday showed that the magnitude of the electromotive force (EMF) generated in a conductor forming a closed loop is proportional to the rate of change of the total magnetic flux passing through the loop (Faraday's law of induction). Thus, for a typical inductance (a coil of conducting wire), the flux linkage is equivalent to magnetic flux ...
Faraday's law is a single equation describing two different phenomena: the motional emf generated by a magnetic force on a moving wire (see the Lorentz force), and the transformer emf generated by an electric force due to a changing magnetic field (described by the Maxwell–Faraday equation).
When a conductive loop experiences a changing magnetic field, from Lenz's law and Faraday's law, the changing magnetic field generates an electromotive force (EMF) around the circuit. For a sinusoidal excitation, this EMF is 90 degrees phased ahead of the field, peaking where the changes are most rapid (rather than when it is strongest):
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 ...
The fundamental basis for induced voltage in a magnetic field comes from Faraday's law describing an induced electromotive force (EMF) as follows: Emf = -N (āΦb / āt) (Nave, C. R. 2011). This states that as the number of magnetic flux lines increase or decrease there is a subsequent change in induced voltage of negative or positive polarity.