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

## 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 longer lengths. This concept is analogous to electrical conductance in the electric circuit.

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

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

which can also be re-written:

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

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):

${\displaystyle {\mathcal {F}}=\Phi _{B}{\mathcal {R}}=NI}$

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):

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

where:

μ, permeability of material,
A, cross-sectional area,
${\displaystyle \ell }$, 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.