In electrical engineering the term flux linkage is used to define the interaction of a multi-turn inductor with the magnetic flux as described by the Faraday's law of induction.

Since the contributions of all turns in the coil add up, in the over-simplified situation of the same flux

[1] The physical limitations of the coil and the configuration of the magnetic field make some flux to leak between the turns of the coil, forming the leakage flux[2] and reducing the linkage.

, where MMF is the magnetomotive force and R is the total reluctance of the coil.

In circuit theory, flux linkage is a property of a two-terminal element.

It is an extension rather than an equivalent of magnetic flux and is defined as a time integral[citation needed] where

This definition can also be written in differential form as a rate 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, 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., where

The simplest example of such a system is a single circular coil of conductive wire immersed in a magnetic field, in which case the flux linkage is simply the flux passing through the loop.

The distinction relies heavily on intuition, and the term "flux linkage" is used mainly in engineering disciplines.

Theoretically, the case of a multi-turn induction coil is explained and treated perfectly rigorously with Riemann surfaces: what is called "flux linkage" in engineering is simply the flux passing through the Riemann surface bounded by the coil's turns, hence no particularly useful distinction between flux and "linkage".

Nevertheless, this is not true, especially for the case of memristor, which is also referred to as the fourth fundamental circuit element.

In addition, for a memristor, the energy related to the flux linkage is dissipated in the form of Joule heating, instead of being stored in magnetic field, as done in the case of an inductance.