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Magnetic permeability of air compared to ferrous materials

  1. Mar 23, 2013 #1
    The answer I'm hoping to achieve from this discussion is how high a field applied to air has to be in order for it's magnetic flux to match the magnetic flux of a ferrous material.

    As you may know, ferrous materials are used as magnetic cores, but once the applied field reaches a certain value, the magnetic flux inside that ferrous material becomes saturated and no longer increases. However, no matter how high a field is applied to air, it always increases linearly (not positive about this).

    Here's a graph of what I'm trying to illustrate:

    If you notice in the graph, uf(ferrous permeability) starts to level out at a certain H value. However, u0(permeability of air) continues to increase linearly. Can anyone help me find the H value where air and ferrous materials meet?
  2. jcsd
  3. Mar 23, 2013 #2
    Brush up on your graph analysis skills. The slope of Magnetic induction (B) v/s Magnetic field strength(H) curve gives you the value of "u". In case of linear magnetic substances this slope is constant( hence the name linear). In case of ferromagnetic substances, u itself is a function of the magnetic field strength.

    As for your question, I CAN help you find the solution to where the curves for air and iron meet and that's fairly simple: As you increase the magnetic field strength, the magnetic Induction settles down on a particular constant value. (lets call it B) then for air,
    B=u0*H. This will give you the co-ordiantes.

    However if you wish to find the condition where both the "u" s equate d(B)/d(H) and u0. which will give you the values on the curve (for the ferromagnetic substance) for which this is true. Note that it isn't necessary that this point be the intersection point of the two curves.
  4. Mar 24, 2013 #3
    First of all, I think it's rude and discouraging to criticize one's analytical skills when you try to help them. Obviously "u" is the slope of the curve. I guess I did not emphasize my main concern correctly. By the way, I'm no physicist, and I'm new to this stuff so please be patient. I'm looking for help.

    I didn't know for sure that I could assume "u0" is constant, regardless of the strength of the magnetic field. That little graph is the only thing that contributed to that assumption. I can't grasp how magnetic flux works through air and how it's different that the alignment of unpaired electrons in metal. Why can't air become saturated?

    I like to think conceptually, and so far I'm visualizing magnetism as a continuous river between poles. Perhaps this analogy is completely off. As I understand it, this "river" can be directed like a piping system.

    Another question to validate the way I perceive magnetism:

    Lets say you have two core-less solenoids with their north poles facing each other, with another core-less solenoid facing perpendicular to them. The south pole of the perpendicular magnet is facing the north ends of the other magnets. Can the perpendicular magnet force the flux of the other magnets through it's center? If set up correctly, could it allow means for a path of less "magnetic resistance"?
  5. Mar 24, 2013 #4


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    Well, you could say "air is always saturated". It (nearly) ignores the external magnetic field.
    The saturated iron will not stay exactly at that magnetic field value if you keep increasing H, but the ferromagnetic effect will not continue to increase B more than "usual" (air, ...) in that region.

    Magnetic field lines are always closed.
  6. Mar 24, 2013 #5
    Can you direct a closed loop of magnetic field using core-less solenoids? I know you can do it with iron, because iron has less magnetic reluctance than air, which I understand to be like a wire having less electric resistance.

    This picture shows the magnetic flux being redirected in a square path:

    If you were to put four core-less electromagnets in a square configuration, would they have the same effect of redirecting the magnetic flux? Would the lumen of these electromagnets have less magnetic reluctance than the air around them because their flux path?
  7. Mar 24, 2013 #6


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    With a proper coil geometry, sure. It works better with iron, however.
    Not as good as in the image.
  8. Mar 25, 2013 #7
    Thank you for all the great advice. I now have a better understanding of how magnetic flux works through air.
  9. Mar 26, 2013 #8
    I was trying to help you. I just made a comment that you had perhaps you had interpreted the graph incorrectly.

    Ferromagnetic substances saturate off because beyond a point the "domains" cannot be more aligned with the applied magnetic field http://en.wikipedia.org/wiki/Saturation_(magnetic)

    Air being majorly composed of Nitrogen (N2) and Oxygen (O2) is paramagnetic and although the relationship between Induced magnetic field and the applied field strength is linear, the slope is very small-almost negligible and contributes essentially nothing to the magnetic field which, is what mfb meant when he said that air is almost always saturated.

    Relax I'm as new to this as you are. Look at the difference in the numbers of our posts :wink:
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