What Is Magnetic Permeability? - Definition & Examples

Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

You may have run across a constant called the permeability of free space in your studies of physics. This constant is intrinsically related to magnetic permeability, and in this lesson, you'll learn what that is and how exactly the two are related.

Magnetic Field and Flux

If you've already studied a little bit about electricity and magnetism you will have learned that magnetic fields are created by electric current. These magnetic fields are represented by magnetic field lines which show the direction and strength of the magnetic field.

The arrows show the direction of the magnetic field around a dipole, and the denser the field lines the stronger the field at that point.
magnetic field of a dipole

The number of these field lines that are passing through a given area is known as magnetic flux. You may have seen the magnetic field (H) and the density of magnetic flux (B) related through the following equation.

magnetic field and flux formula

Here μ is magnetic permeability. If this sounds familiar to you it's because you've probably worked with a constant related to it called the permeability of free space. In the past, you would have simply handwaved this constant away as just some number, but it has a purpose. Now, it's time to learn what magnetic permeability and the permeability of free space represent, and how they're related.

Magnetic Permeability

The best thing we can compare magnetic permeability to for you to understand it easily is conductivity. With conductivity, you know some materials allow electricity to pass through them better than others. For example, copper is a much better conductor than rubber.

Magnetic permeability is a similar concept to this, but for magnetic flux instead of electricity. The higher the magnetic permeability the better the material allows for magnetic flux to pass through it.

A chart of some common magnetic permeabilities measured in Henries per meter.
magnetic permeability chart

The permeability of free space (μ0) we talked about earlier is actually just the magnetic permeability associated with a vacuum, i.e. the permeability of a magnetic field in the absence of any material. This is an important quantity in physics and it shows up in many relations. Examples of this include the speed of light in a vacuum, Ampere's law, and magnetic inductance.

permeability of free space equations

Magnetic Materials

When viewing the magnetic permeability of a material you'll find that it is often given as relative magnetic permeability (μr). This is simply the ratio of magnetic permeability to the permeability of free space.

relative permeability equation

Relative magnetic permeability comes into play when looking at the types of magnetism a material can exhibit. When a material has a relative magnetic permeability less than one it is diamagnetic. This means that when the material is in the presence of a magnetic field it partially expels that field. Oppositely, paramagnetic materials take in the magnetic field it is in the presence of, and have a relative magnetic permeability greater than one. Finally, ferromagnetic materials work like paramagnetic materials except their magnetic properties remain after the magnetic field they are in is removed. Also, the magnetic permeability of ferromagnetic materials tends to be high.

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