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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: 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 P is defined as the reciprocal of magnetic reluctance R (in analogy with the reciprocity between electric conductance and resistance): ${\mathcal {P}}={\frac {1}{\mathcal {R}}}$

which can also be re-written: ${\mathcal {P}}={\frac {\Phi _{\mathrm {B} }}{NI}}$

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): ${\mathcal {F}}=\Phi _{\mathrm {B} }{\mathcal {R}}=NI$

where:

$Φ B$ , 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,
ℓ, magnetic path length.

The SI unit of magnetic permeance is the henry (H), equivalently, webers per ampere.^[a]

Materials science

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

Notes

^ The SI unit of mmf is the ampere, the same as the unit of current (analogously the units of emf and voltage are both the volt). Informally, and frequently, this unit is stated as the ampere-turn to avoid confusion with current. This was the unit name in the MKS system.

References

Electromagnetism

Properties of Magnetic Materials (units of magnetic permeance)

Material science

Bombaru, D., Jutras, R., and Patenaude, A., "Air Permeance of Building Materials". Summary report prepared by, AIR-INS Inc. for Canada Mortgage and Housing Corporation, Ottawa, 1988.

[1] The SI unit of mmf is the ampere, the same as the unit of current (analogously the units of emf and voltage are both the volt). Informally, and frequently, this unit is stated as the ampere-turn to avoid confusion with current. This was the unit name in the MKS system.

[a]

@@ Line 1: / Line 1: @@
+{{Electromagnetism|Magnetic circuit}}
-'''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: <math>\mathcal{P}</math>, or capital lambda Λ.
+'''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):
-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]].
+<math display="block">\mathcal{P} = \frac{1}{\mathcal{R}}</math>
-Magnetic permeance <math>\mathcal{P}</math> is defined as the reciprocal of magnetic reluctance <math>\mathcal{R}</math> (in analogy with the reciprocity between electric conductance and resistance):
-<math>\mathcal{P} = \frac{1}{\mathcal{R}}</math>
 which can also be re-written:
+<math display="block">\mathcal{P} = \frac{\Phi_\mathrm{B}}{NI}</math>
+using [[magnetic circuit #Hopkinson's law: the magnetic analogy to Ohm's law|Hopkinson's law]] (magnetic circuit analogue of [[Ohm's law]] for electric circuits) and the definition of [[magnetomotive force]] (magnetic analogue of [[electromotive force]]):
-<math>\mathcal{P} = \frac{\Phi}{NI}</math>
+<math display="block">\mathcal{F} = \Phi_\mathrm{B} \mathcal{R} = NI</math>
+where:
-using [[Magnetic circuit #Hopkinson's law: the magnetic analogy to Ohm's law|Hopkinson's law]] (magnetic circuit analogue of [[Ohm's law]] for electric circuits) and the definition of [[magnetomotive force]] (magnetic analogue of [[electromotive force]]):
+* {{math|Φ<sub>B</sub>}}, [[magnetic flux]],
+* {{mvar|I}}, current, in amperes,
+* {{mvar|N}}, [[winding number]] of, or count of turns in the electric coil.
+Alternatively in terms of [[permeability (electromagnetism)|magnetic permeability]] (analogous to [[electric conductivity]]):
-<math> \mathcal{F} = \Phi_B \mathcal{R} = NI </math>
+<math display="block">\mathcal{P} = \frac{\mu A}{\ell}</math>
+where:
-Where: <br />
+* {{mvar|μ}}, permeability of material,
-''Φ<sub>B</sub>'' = [[Magnetic flux]] <br />
+* {{mvar|A}}, cross-sectional area,
-''NI'' = Current-turns, (current) × (number of turns of conductor to make a coil).
+* ℓ, magnetic path length.
+The SI unit of magnetic permeance is the [[henry (unit)|henry]] (H), equivalently, [[weber (unit)|webers]] per [[ampere]].{{efn|The SI unit of [[magnetomotive force|mmf]] is the ampere, the same as the unit of current (analogously the units of [[electromotive force|emf]] and voltage are both the volt). Informally, and frequently, this unit is stated as the ampere-turn to avoid confusion with current. This was the unit name in the [[MKS system]].}}
-Alternatively in terms of [[Permeability (electromagnetism)|magnetic permeability]] (analogous to electric conductance):
-<math>\mathcal{P} = \frac{\mu A}{\ell}</math>
-Where: <br />
-''μ'' = Permeability of material<br />
-''A'' = Cross-sectional area<br />
-<math>\ell</math> = Length of conductor in circuit
-The SI unit of magnetic permeance is "webers per ampere-turn", that is Wb A<sup>-1</sup>.
 ==Materials science==
+In [[materials science]], '''permeance''' is the degree to which a material transmits another substance.
-In [[Materials science]], '''permeance''' is the degree to which a material transmits another substance.
 ==See also==
@@ Line 40: / Line 37: @@
 *[[Reluctance]]
+==Notes==
-==External articles and references==
+{{notelist}}
+==References==
 ===Electromagnetism===
 * [http://orca.phys.uvic.ca/~tatum/elmag/em12.pdf ''Properties of Magnetic Materials''] (units of magnetic permeance)
@@ Line 46: / Line 46: @@
 ===Material science===
 * Bombaru, D., Jutras, R., and Patenaude, A., "''Air Permeance of Building Materials''". Summary report prepared by, AIR-INS Inc. for [[Canada Mortgage and Housing Corporation]], Ottawa, 1988.
-{{Physics-stub}}
 [[Category:Electric and magnetic fields in matter]]