# Permeance

Permeance, in general, is the degree to which a material admits a flow of matter or energy. Permeance is usually represented by a curly (calligraphic) capital P: $\mathcal{P}$, or capital lambda Λ.

## Electromagnetism

In electromagnetism, permeance is the inverse of reluctance. Permeance is a measure of the quantity of flux for a number of current-turns in magnetic circuit. A magnetic circuit almost acts as though the flux is 'conducted', therefore permeance is larger for large cross sections of a material and smaller for longer lengths. This concept is analogous to electrical conductance in the electric circuit.

Magnetic permeance $\mathcal{P}$ is defined as the reciprocal of magnetic reluctance $\mathcal{R}$ (in analogy with the reciprocity between electric conductance and resistance):

$\mathcal{P} = \frac{1}{\mathcal{R}}$

which can also be re-written:

$\mathcal{P} = \frac{\Phi}{NI}$

using Hopkinson's law (magnetic circuit analogue of Ohm's law for electric circuits) and the definition of magnetomotive force (magnetic analogue of electromotive force):

$\mathcal{F} = \Phi_B \mathcal{R} = NI$

Where:
ΦB = Magnetic flux
NI = Current-turns, (current) × (number of turns of conductor to make a coil).

Alternatively in terms of magnetic permeability (analogous to electric conductance):

$\mathcal{P} = \frac{\mu A}{\ell}$

Where:
μ = Permeability of material
A = Cross-sectional area
$\ell$ = Length of conductor in circuit

The SI unit of magnetic permeance is "webers per ampere-turn", that is Wb A-1.

## Materials science

In Materials science, permeance is the degree to which a material transmits another substance.