# 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 capital P: ${\mathcal {P}}$ .

## Electromagnetism

In electromagnetism, permeance is the inverse of reluctance. In a magnetic circuit, permeance is a measure of the quantity of magnetic flux for a number of current-turns. 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 smaller cross section 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:

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

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,
I, current, in amperes,
N, winding number of, or count of turns in the electric coil.

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

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

where:

μ, permeability of material,
A, cross-sectional area,
$\ell$ , magnetic path length.

The SI unit of magnetic permeance is the henry (H), that is webers per ampere-turn.

## Materials science

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