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# Physics/The value for relative permeability of an electromagnet's core

Question
Hello,

Thank you for all your helpful answers recently. I am having some trouble calculating the strength of an electromagnet and I am wondering if you can clear up some points of confusion.

I am using the following formula

Magnetic field = permeability x turn density x current

I am just wondering about two things. First, if my electromagnet has only one coil - actually 3/4 of a coil. In this case, would this formula still apply, or do I need to use a different method of calculating the magnetic field?

Also, I am not sure what value to put for the permeability.
I have read that this value should be the relative permeability of the core material eg iron multiplied by the relative permeability of air, is that correct? If the electromagnet is coated in another material, for example copper, would the permeability value change? Would I need to add the relative permeability of copper somewhere into the equation? Is there a way the permeability of the core could be increased by insulating the entire magnet in another material?

Actually, I am having trouble finding out the relative permeability of iron - some websites say it is 200, others (http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/#mur) give the value as 5000. Other websites (http://hyperphysics.phy-astr.gsu.edu/hbase/tables/magprop.html#c2) talk about   the "maximum relative permeability" of iron, and I am not sure how the permeability is changed/increased.
I am just not sure what value of permeability to put into the equation (assuming that equation can be used for my hypothetical one coil electromagnet).

Can you tell me how I can calculate the permeability for the equation, and whether there is anything I can do to make the magnet stronger in terms of the material used for the core?

Thank you again and best regards,
Eddie

Hello Eddie,

In the formula that you listed, "turn density" is meant to be (number of turns) / (length of solenoid). The unit required for the length is meters, so your turn density will be quite small.
Go to the website
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
Notice what it says in bold print to the right side of the top about the field outside. The formula
Magnetic field = permeability x turn density x current
is intended to apply to the field inside the tube of the solenoid. So the term solenoid applies only slightly to the electromagnet you describe. And likewise, that formula applies only slightly. So yes, I think you need need to use a different method of calculating the magnetic field.

Go to the site
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html
Now picture this. Orient the wire horizontal on a table and bend it into 3/4 of a loop. And let the current in the wire be flowing counter-clockwise. If you apply the right hand rule on one part of the wire, and then slide your hand around the arc, your fingertips will always be pointing up in the center of the arc. So an upward magnetic field is reinforced by the current throughout the arc. Now, I don't know how far above the surface of the table you would be able to measure an upward magnetic field. Because, as the above website shows, the field near any part of the arc wants to circle the nearby wire.

The permeability should be the relative permeability of the core material eg iron multiplied by the permeability (not relative permeability) of vacuum. Air and vacuum are essentially the same for this purpose. From Wikipedia: "In SI units, permeability is measured in henrys per meter (H·m−1), or newtons per ampere squared (N·A−2)."

I can't picture what "coat the electromagnet in copper or some other material", would look like. So I can't say anything about those "coating" ideas.

I also am not sure how the permeability is changed/increased in the various tables. I think it may be some heat treatment and other special handling. It seems 200 is a good number for basic iron. There are materials with significantly higher permeability than basic iron. These sites list possibilities:
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html#c5
http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/magprop.html

I hope this helps,
Steve
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Physics

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#### Steve Johnson

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