Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Flux linkage

Flux linkage is a property of a two-terminal element. Although it is often confused with magnetic flux, the Flux linkage is actually an extension rather than an equivalent of magnetic flux. Flux linkage is defined as

lambda=int_, v, dt

where v is the voltage across the device or the potential difference between the two terminals. This definition can also be written in differential form as

v = frac{dlambda}{dt}

Faraday showed that the magnitude of the 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). Thus, for a typical inductance (a coil of conducting wire), the flux linkage is equivalent to magnetic flux, which is the total magnetic field passing through the surface (i.e. normal to that surface) formed by a closed conducting loop coil, and is determined by the number of turns in the coil and the magnetic field,i.e.,

lambda=intlimits_S, vec{B} cdot dS

where vec{B} is the flux density, or flux per unit area at a given point in space.

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