Magnetic Flux Linkage

in electrical technology, the total magnetic flux Ψ linked with a particular circuit.

In essence, the magnetic flux linkage always has the same value as the flux in the integral definition:

ϕ = ∫ B̄ dS̄ = ψ

where B̄ is the magnetic induction vector and S̄ is the surface bounded by the circuit for which the magnetic flux linkage is being determined. The above statement is also valid for a multiturn inductance coil whose series-connected turns form a single circuit (Figure 1).

Figure 1

In this case, the total flux, or the flux linkage, is

where k= (1, …, w) numbers the turns with which the flux Φ_k is coupled. In the simplest case, for example, for a uniformly wound toroid, Ψ = w*Φ, where Φ is the flux through the transverse cross section of the magnetic circuit, or core.