Magnetic Flux.  The total magnetization resulting from a magnetizing force is called the magnetic flux, and is analogous to current.  The intensity of a magnetic flux is expressed by the number of magnetic lines of force in a square centimeter or square inch.

While the magnetomotive force or magnetizing force of a given helix is independent of the material of the core, the flux which it sets up is largely dependent on the material and shape of the core—­not only upon this but on the material that lies in the return path for the flux outside of the core.  We may say, therefore, that the amount of flux set up by a given current in a given coil or helix is dependent on the material in the magnetic path or magnetic circuit, and on the shape and length of that circuit.  If the magnetic circuit be of air or brass or wood or any other non-magnetic material, the amount of flux set up by a given magnetizing force will be relatively small, while it will be very much greater if the magnetic circuit be composed in part or wholly of iron or steel, which are highly magnetic substances.

Permeability.  The quality of material, which permits of a given magnetizing force setting up a greater or less number of lines of force within it, is called its permeability.  More accurately, the permeability is the ratio existing between the amount of magnetization and the magnetizing force which produces such magnetization.

The permeability of a substance is usually represented by the Greek letter mu (pronounced mu).  The intensity of the magnetizing force is commonly symbolized by H, and since the permeability of air is always taken as unity, we may express the intensity of magnetizing force by the number of lines of force per square centimeter which it sets up in air.

Now, if the space on which the given magnetizing force H were acting were filled with iron instead of air, then, owing to the greater permeability of iron, there would be set up a very much greater number of lines of force per square centimeter, and this number of lines of force per square centimeter in the iron is the measure of the magnetization produced and is commonly expressed by the letter =B=.

From this we have

 mu = B/H

Thus, when we say that the permeability of a given specimen of wrought iron under given conditions is 2,000, we mean that 2,000 times as many lines of force would be induced in a unit cross-section of this sample as would be induced by the same magnetizing force in a corresponding unit cross-section of air.  Evidently for air B = H, hence mu becomes unity.

The permeability of air is always a constant.  This means that whether the magnetic density of the lines of force through the air be great or small the number of lines will always be proportional to the magnetizing force.  Unfortunately for easy calculations in electromagnetic work, however, this is not true of the permeability of iron.  For small magnetic densities the permeability is very great, but for large densities, that is, under conditions where the number of lines of force existing in the iron is great, the permeability becomes smaller, and an increase in the magnetizing force does not produce a corresponding increase in the total flux through the iron.