# Magnetic Permeability -Definition, Formula, Units, Types

Magnetic permeability is the magnetization capability of the material that allows the magnetic line of force to pass through it. In other words, magnetic permeability supports the formation of a magnetic field. The material’s magnetic permeability determines the amount of magnetic flux passing through it. It is denoted by the Greek letter µ.

## Magnetic Permeability Definition

Magnetic permeability is defined as the ratio of the magnetic flux density to the magnetic intensity. It is also called Permeability of Medium

It is a scalar quantity that has only magnitude. The magnetic permeability of the material shows the degree of the magnetic field penetration through a material. The material that strongly supports the magnetic lines of force has greater magnetic permeability. In other words, the higher permeability material has a lesser conductivity for magnetic lines of force.

The magnetic permeability of the soft iron is much more than the air. The soft iron quickly passes most of the magnetic force of lines because the ring provides an easy path to the magnetic lines. Thus, the magnetic permeability is proportional to the number of lines passing through the material.

The permeability of the air or vacuum is very poor. The passing of the magnetic field of lines through the air is shown below. The air provides more impedance to the magnetic force of lines. Therefore, the permeability of air is very poor.

The permeability of the air or vacuum or free space is equal to 4π×10-7 H/m≈ 12.57 🗙 10⁻⁷ H/m, and it is represented by μ0

## Magnetic Permeability Formula

The formula of magnetic permeability of medium is;

The formula of permeability of free space or air or vacuum is;

## Unit of Magnetic Permeability

Their SI unit is Henry per meter (H/M) or newton per ampere square (N-A-2).

## Types of Permeability

The different types of permeability are as follows;

### Permeability of Free Space

Permeability of free space or air or vacuum is the ratio of magnetic intensity in a vacuum and magnetizing field. It is represented by;

μ0=B0/H

The ratio of magnetic intensity in a vacuum and magnetizing field.

### Permeability of Medium

It is the ratio of magnetic intensity in the medium and magnetizing field. Its formula is;

μ = B/H

## Relative Permeability

Relative permeability is the comparison of the permeability of the medium to air. The permeability of air is 4π×10-7 H/m which is very low. Relative permeability shows how many times the permeability of the medium is compared to the permeability of the air.

The ratio of the permeability of the medium to the permeability of air is called relative permeability. It is the ratio quantity and therefore it is dimensionless.

The formula of relative permeability is shown below.

From the above formula, the relative permeability of the air and the non-magnetic material is equal to one.

The relative permeability can also be expressed in terms of the magnetic field density of material and vacuum.

The permeability of the medium or material is:

## Factors affecting magnetic permeability

The following factors affect permeability.

1. Temperature
2. Humidity
3. Nature of the material
4. position in the medium
5. Frequency of the applied field

## Solved Problems on Magnetic Permeability

### The primary winding of 400 turns carries a current of 1.8 A. On reversal, a change of 8 × 10−3 Wb-turns is recorded in the secondary winding of 10 turns. The ring has a cross-sectional area of 2.5 × 10−4 m2 and a length of 0.75m2. Assuming uniform flux distribution, determine the value of the permeability.

Rate of Change of flux, 2Φ N2= 8 x 10-3 wb-turns
flux(Φ) = (8 X 10-3 )/(2X10) Wb-turns
=4 X 10-4 Wb-turns

B= Φ/A
= (4 x 10-4)/(2.5 X10-4 )
= 1.6 Wb/m2

The magnetic field Intensity(H)
H = NI/L
= (400 X 1.8)/0.75
= 960 AT/m

### Permeability(µ)µ=µ0µrµr=µ/µ0 =B/µ0H = 1.6/(4π×10-7X960) µr = 1320A core of a transformer is made up of soft iron of relative permeability µr = 9000. Determine the absolute permeability of the core.

µr = 9000
µ0 =4π×10-7 H/m

Absolute permeability of transformer core

µ=µ0µr
µ = 4π×10-7 X 9000
µ = 1.13×10-2 H/m