Permeability
μH
/m
Substance (optional)
Ferrite
Relative permeability
Susceptibility

# Magnetic Permeability Calculator

By Dominik Czernia, PhD candidate

The magnetic permeability calculator is a tool that will help you determine the dependency between magnetic permeability and susceptibility. In the following text, we have explained what is permeability and presented how you can calculate it using the permeability definition. Read on if you want to find out why some materials are magnetic and some are not.

Did you know that there are substances, called superconductors, which have an unusual property that allows them to levitate in a magnetic field? Isn't it fascinating? That's why we have also answered the question of what is a superconductor.

## What is permeability?

According to the permeability definition, it describes a magnetic field produced by the material that arises in response to an applied magnetic field. We divide materials into three main types based on the magnetic permeability `µ`:

• in diamagnetic materials an externally applied magnetic field creates an internal magnetic field with opposite direction, causing a repulsive effect. Their magnetic permeability is less than the magnetic permeability of free space `µ₀`.
• paramagnetic materials have the magnetic permeability greater than `µ₀`, but its internal magnetic field arises only in the presence of an external magnetic field. The magnetic field attracts them.
• ferromagnetic materials have magnetic permeability much greater than `µ₀`, and they can retain their internal magnetic field even in the absence of an external magnetic field. Ferromagnetism is the mechanism that forms permanent magnets in specific materials, e.g., one of the strongest - a neodymium magnet.

Do you know what is the microscopic origin of the magnetism of matter? Check our magnetic moment calculator to learn how you can compute an elementary magnetic moment of an atom.

## Magnetic permeability and susceptibility

In magnetism we use three fields:

• magnetization `M` which is the magnetic field created by the material,
• magnetic field `H` which is the magnetic field from the outside of the material,
• magnetic field `B` which is the total magnetic field inside the material.

And these fields are closely related to each other:

• `B = µ * H`, where `µ` is the permeability,
• `M = χ * H`, where `χ` is the magnetic susceptibility (check Curie's law calculator),
• `B = µ₀ * (H + M)`, where `µ₀ = 4 * π * 10^(-7) H/m` is the magnetic permeability of free space. The unit `H` is called "henry" and it is an unit of inductance (check solenoid inductance calculator).

Our magnetic permeability calculator provides a conversion between `µ` and `χ` which results from the above equations:

`χ = µ / µ₀ - 1 = µᵣ - 1`

We usually use so-called relative permeability `µᵣ = µ / µ₀` to simplify the notation. Try our magnetic permeability calculator and see how it works!

## What is a superconductor?

Physical properties of some materials sharply change when cooled below a characteristic critical temperature. Their electrical resistance and permeability become exactly zero, and therefore they are called superconductors. A material with zero permeability behaves like an ideal diamagnetic which completely ejects a magnetic field from the interior of superconductor, and we can observe the levitation phenomenon. Perhaps the dreams of levitating cars will soon come true?

Dominik Czernia, PhD candidate

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