# permeability

#### gorgondrak

Joined Nov 17, 2014
61
Volume I chapter 14 in DC says that permeability is the, "measure of a material's acceptance of magnetic flux". Wikipedia says about the same thing, "the degree of magnetization of a material in response to a magnetic field". The AAC book goes on to say, "greater permeability means easier passage of magnetic flux". That's the part I don't understand. If a conductive material is becoming magnetized in response to a magnetic field doesn't that mean that less of the field is getting out and more is being retained? I understand permeability to be a bad thing in a wire because the electrons will be magnetizing the line in front of them as they are moving making it more difficult for them to travel. So low permeability will mean less opposition to current (relative permeability of iron is 5000 while copper is only .999, http://en.wikipedia.org/wiki/Permeability_(electromagnetism)) Low permeability means the material is not retaining the magnetization of the field allowing the current to move more easily. So if greater permeability mean easier passage of magnetic flux and the magnetic fields are escaping the wire more easily providing less opposition than why do materials with low permeability allow more current which seems analogous to 'one of' the equations for characteristic impedance sqrt of permeability/permittivity. As permeability goes up impedance goes up, limiting the current. What I would expect with the conductive material retaining the magnetic field providing opposition. It seems that less permeability would mean easier passage of magnetic flux out of the material with less being retained to impede current flow.

#### sirch2

Joined Jan 21, 2013
1,029
It indicates how permeable a material is to magnetic flux, which is NOT the same as current flow. Permittivity gives the measure of resistance to an electric field.

Note the two words, permeability and permittivity, are confusingly similar.

#### studiot

Joined Nov 9, 2007
4,998
To resolve your apparent paradox in the magnetic field think about the idea of "the line of least resistance".

Nature often adopts the line of least resistance philosophy, which basically runs "the XXX quantity" follows the line of least resistance and you will find this embodied in classical and quantum mechanics, electrical current theory, general relativity, and in your particular case, electrodynamic theory.

In electrical current theory if you connect two resistors one of 1 ohm and one of 10 ohms across a voltage source, the majority of the flux (current) will flow through the line of least resistance or the 1 ohm resistor.

So it is with magnetic flux.

The majority of the magnetic flux will flow through the line of least resistance. In the case of magnetic flux this is measured by the 'reluctance' of the medium.

http://en.wikipedia.org/wiki/Magnetic_reluctance

#### alfacliff

Joined Dec 13, 2013
2,458
and the magnetic field does not "escape " the wire, it circles it. unless you are talking about an electromagnetic (rf ) field, when it can escape wiith an electric field.

#### MrAl

Joined Jun 17, 2014
8,157
Volume I chapter 14 in DC says that permeability is the, "measure of a material's acceptance of magnetic flux". Wikipedia says about the same thing, "the degree of magnetization of a material in response to a magnetic field". The AAC book goes on to say, "greater permeability means easier passage of magnetic flux". That's the part I don't understand. If a conductive material is becoming magnetized in response to a magnetic field doesn't that mean that less of the field is getting out and more is being retained? I understand permeability to be a bad thing in a wire because the electrons will be magnetizing the line in front of them as they are moving making it more difficult for them to travel. So low permeability will mean less opposition to current (relative permeability of iron is 5000 while copper is only .999, http://en.wikipedia.org/wiki/Permeability_(electromagnetism)) Low permeability means the material is not retaining the magnetization of the field allowing the current to move more easily. So if greater permeability mean easier passage of magnetic flux and the magnetic fields are escaping the wire more easily providing less opposition than why do materials with low permeability allow more current which seems analogous to 'one of' the equations for characteristic impedance sqrt of permeability/permittivity. As permeability goes up impedance goes up, limiting the current. What I would expect with the conductive material retaining the magnetic field providing opposition. It seems that less permeability would mean easier passage of magnetic flux out of the material with less being retained to impede current flow.
Hi,

The electrical circuit equivalent to the magnetic circuit permeability is the conductivity which i'll explain here.

You know how resistance in an electrical circuit affects the circuit operation: when the resistance decreases the current flows more easily.
The resistance of a bar of material can be calculated from:
R=L/(c*A)

where
R is the resistance from one end to the other,
L is the length,
A is the cross sectional area,
c is the conductivity, a measure of how well a material conducts current.

From the above we can see that as the conductivity goes up the resistance goes down because 'c' is in the denominator.

Well the magnetic circuit equivalent to resistance is reluctance, and so as the reluctance decreases the flux flows more easily.
So now you know how reluctance (but not permeability) affects the magnetic circuit. Now you are ready to look at the permeability.

The reluctance is related to the permeability as follows:
R=L/(u*A)

where
R is the reluctance,
L is the length of the material (core for example),
A is the cross sectional area of the material (core), and
u is the permeability.

From the above equation, we can see that as the permeability goes up the reluctance goes down because the permeability 'u' is the denominator of that equation. And we know that when the reluctance goes down the flux can increase. So by extension we can see that as the permeability goes up the flux can increase.

You can examine both equations and see how similar they are to each other, so if you understand one you should be able to understand the other.

#### alfacliff

Joined Dec 13, 2013
2,458
the magnetic field in a conducting wire is not through the wire, it is around the wire. for the field to penetrate the wire, it muxt come from outside. that is how inductance in coils work, the wires cutting the magnetic field from the other turns. while a single wire has inductance, it is not very much.

#### gorgondrak

Joined Nov 17, 2014
61
And this reluctance impedes the current as a series inductance?

#### studiot

Joined Nov 9, 2007
4,998

#### alfacliff

Joined Dec 13, 2013
2,458
And this reluctance impedes the current as a series inductance?
only on ac current.

#### t_n_k

Joined Mar 6, 2009
5,455

#### alfacliff

Joined Dec 13, 2013
2,458
th old time telegraph circuits ran on dc through iron wire, and had no problems with magnetic effects ro permability. you dont get a magnetic field down the wire, its wrapped around it.