# Magnetic Permeability Formula, Calculation & Calculator

### Magnetic Permeability Calculator:

A magnetic permeability calculator is a tool that helps you determine the relationship between magnetic permeability and susceptibility.

Permeability, by definition, describes the magnetic field created by a material that arises in response to an applied magnetic field. We divide materials into three main categories based on the magnetic permeability µ.

In magnetic materials an externally applied magnetic field creates an internal magnetic field in the opposite direction. It has a repellent effect. Their magnetic permeability is µ₀ less than the magnetic permeability of free space. Paramagnetic materials have magnetic permeability greater than µ₀, but their internal magnetic field arises only in the presence of an external magnetic field. A magnetic field attracts them.

Ferromagnetic materials have a magnetic permeability greater than µ₀ and can retain their internal magnetic field even in the absence of an external magnetic field. Ferromagnetism is the mechanism of creating permanent magnets in certain materials, eg, a strong one – a neodymium magnet. Do you know what the microscopic appearance of the magnetism of matter is? To learn how to calculate the fundamental magnetic moment of an atom, see our Magnetic Moment Calculator.

### Magnetic Permeability and Susceptibility:

Magnetic permeability and susceptibility X is equal to the permeability μ(H/m) in Henry per meter and divided permeability μ0(H/m) and minus 1 is equal to the μr(H/m) in Henry per meter and minus one -1.Hence the magnetic permeability and susceptibility can be written as

X= μ(H/m) / μ0(H/m) -1 = μr(H/m)-1

B= μ *H

Μ =B/H

B=μ * (H+M)

Magnetization M=X*H

Where

M=is the magnetization which is the magnetic field created by the material

H= is the magnetic field from the outside of the material

B=is the total magnetic field inside the material

X=is the magnetic susceptibility

μ =is the permeability

μ=4 π *10-7 H/m is the magnetic permeability of free space

Relative permeability is the ration  of  permeability of the substance to the permeability of free space

μ r = μ / μ

The relation between magnetic permeability and susceptibility is given here

X= μ / μ -1 = μr-1

A material that has exactly zero permeability and electrical resistance is called the superconductor .The physical properties of materials change when it is cooled below the characteristic crictica temperature

### Example:1

If the magnetic permeability of a substance is 250 μ H/m.Find the relative permeability and susceptibility?

Given that

Magnetic permeability of a substance μ =250 μ H /m

Relative permeability μr = μ / μ

=250 /4 π *10-7

=5.026

Magnetic susceptibility x = μr -1

=5.026-1

=0.99968

Therefore, relative permeability of the substance is 5.026

And susceptibility is 0.99968

### Example :2

If the magnetic permeability 125.Find the susceptibility value?

Relative permeability (μr)=125

By using formula

Susceptibility (X) =μr-1

=124