 # Permeability

### What is Permeability?

Permeability is the ability of a material to allow the magnetic flux when the object is placed inside the magnetic field where magnetic flux is the measure of the number of magnetic lines of forces that can pass via a given surface.

• Permeability is denoted by a Greek symbol ‘m’

• m is measured in: Farad / Meter (F/ M).

1. Electromagnetism

2. Magnetomotive force, and the strength of the magnetic field.

3. Types of material: Ferromagnetic, Paramagnetic, and Diamagnetic

4. Permeability: Absolute and Relative

5. Reluctivity.

Let’s take any straight current-carrying conductor or a coil when kept inside the magnetic field allows the magnetic field lines to pass through, which we can find out by Fleming’s left-hand rule.

### Fleming’s Left-Hand Rule:

Fleming’s left - hand rule states that if we stretch the thumb, middle finger and the

The index finger of the left hand in such a way that they make an angle of 90 degrees       (Perpendicular to each other) and the conductor placed in the magnetic field

experiences Magnetic force.

Such that:

1.  Thumb: It points towards the direction of force (F)

2. Middle finger: It represents the direction of the current (I)

3. Index finger:  It represents the direction of the magnetic field (B)

Here, in this image, we can see that the magnetic flux is concentrated more at the center than in the exteriors, which infers that magnetic field strength is directly proportional to the current ‘I’ flowing through the conductor and inversely proportional to the distance.

## For a Straight Wire, the Strength of a Magnetic Field can be Calculated as:

 H (magnetic field strength) = I (current)/ 2* pi * r

And for a coil, it is proportional to the number of turns of wire (N) and the current ’I’ flowing through it, but inversely proportional to the length, ‘L’ of the wire:

H= I × N/ L

Just have a look at the table shown below with the different Relative permeability (mr) values of various types of materials kept in the magnetic field.

## Table 1.1: Value of Relative Permeability (mr) for Some Objects:

 S.No. Object Relative permeability (mr) 1. Wood 1.00000043 2. Aluminium 1.000022 3. Cobalt 250 4. Nickel 600 5. Iron 2, 00, 000

Here, Relative permeability (mr)  computes the efficient permeability of any substance.

Magnetic field intensity of an electromagnet depends upon the material being used, so a medium or a material plays a major role here because the main purpose is to concentrate the magnetic flux inside the field in a particular path.

There are three types of materials: Paramagnetism, Ferromagnetism, and Diamagnetism.

### 1. Paramagnetism:

The paramagnetic property of an element depends on the electronic configuration, and they are weakly attracted to the magnet, and they don’t retain their magnetism after an external magnetic field is removed. The materials such as Magnesium, Molybdenum, Lithium, possess Paramagnetism.

### 2. Diamagnetism:

The electrons in the outer shell of an element are paired in their orbitals that’s why they don’t possess magnetism in themselves as we see in table  1.1 above that the value wool and aluminium as compared to Co, Ni, and Fe are negligible.

### 3. Ferromagnetism:

Any element which has unpaired electrons in its outermost shell such that when it is placed in the magnetic field, possess high magnetic field strength, and retains this attribute even if an external magnetic field is removed.

Table 1.1, shows the strength of the magnetic field of elements like Co, Ni, and Fe.

The element Fe has the highest value, because of its high ability to concentrate a dense magnetic flux around itself.

One thing can be observed that the element, “Fe” behaves as both Paramagnetic and a ferromagnetic as well, why is there a difference?

It all depends upon the composition and the temperature, on the basis on which the electrons are polarized.

At high temperatures, Iron behaves as a paramagnetic material while at low, it behaves as a ferromagnetic material.

The type of material we use decides the amount of work being done, which in turn means the strength of the magnetic field created around the material.

## Permeability:

Any material let’s say Iron when placed inside the magnetic field possesses magnetism in itself.

Here, Iron has an ability to allow magnetic fields with high strength in itself, and that’s why it has high permeability.

While the material like Wood, Aluminium doesn’t allow the magnetic fields to pass via and, they are reluctant to permit magnetism in itself, that’s why they also are calculated regarding permeability of free space or permeability constant.

In simple terms, permeability is an ability of any material to permit the density of the magnetic flux.

### Magnetic Intensity and Intensity of Magnetization:

Magnetic Intensity defines the degree of magnetism (created by a magnetic field) a material can hold in itself.

Calculated as: H (Magnetic field strength) = n * I

Where n = no of turns in the wire

I = The current flowing through the conductor.

and, Intensity of Magnetization of a magnetic material is defined as a magnetic moment per unit volume of the material, which is calculated as:

I = Magnetic moment (A)/ Volume (V).

Which is high for Ferromagnetic material and low for a diamagnetic material.

Permeability solely depends upon the medium being used, so, ‘type of medium’ plays a major role here.

Permeability working can be observed in transformers.

There are Certain Points to Understand How Permeability Depends upon Various Factors Given Below:

### 1. Temperature:

If the temperature of the medium is high, then the strength of the magnetic field will also become low, which means work done will be less.

Temperature  = k/ work  = k/ m  (m is permeability.)

### 2. Field Strength:

Field strength is one of the fundamental physical quantities that measure the intensity of magnetic fields.

If the material isn’t good, then the field strength won’t be good too.

### 3. Field frequency:

If the frequency of supply varies, then, harmonics will develop, which would create a humming sound, which usually happens in the Transformer.

### 4. Humidity:

During summer, when the temperature keeps on changing which in turn creates some variations in the properties of a material, it overall makes changes in the work being done and creates an impact on the permeability as well.

Simply, to increase the strength of the magnetism of the medium that we call it as permeability, m. The material should be of good quality.

If the medium is good, then the work done will also be more, because work done is directly proportional to the strength of the magnetic field and the permeability as well.

### Permeability and its Types: Absolute and Relative.

Iron provides a low reluctance path and helps in the formation of magnetic fields which means, ‘High Permeability.’ It is because the molecular structure on the inside is easily able to induce these magnetic field lines.

Thus, permeability represents how much it would be helpful in energy conservation.Permeability is two types: Absolute and Relative

Magnetic Permeability is the ratio of Magnetic flux density to the field strength.

m= B/ H = Henries/ meter.

Fig. A  shows the direction of the magnetic field around the dipole, which shows that the density of magnetic flux is more at the center than on the exteriors.

In this case, if we put the compass in the magnetic field, then the South Pole of the magnetic needle of the compass would get attracted to the North Pole of the magnet and vice-versa.

But, if there is a case that the medium such as Wood, Aluminium is kept in the place of a dipole, then the needle would show no deflection because there wouldn’t be any change in the magnetic field, which we refer to as the permeability of free space or simply, a permeability constant denoted by m-naught or m-zero.

.

The relative permeability of a magnetic material, designated mr, is the ratio of its absolute permeability m to that of air m-zero.

The absolute permeability (m) of a soft iron core is given as 80 milli-henries/meter. Though the value of m for Iron may have values from 100 to 5000, depending upon the grade of the material.

mr of magnetic materials such as cobalt, nickel, iron, steel, and their alloys are far greater than unity and are not constant, as you can see in Fig. B(2) and Fig. B(3).

The mr of a non-magnetic material, such as air, copper, wood glass, and plastic are, for all practical purposes, equal to unity.

mr = m / m-zero

The value of m-zero = 4 * pi * 10^-7

= 1.257 * 10^-  7.

Q1: What is the Basic Difference Between Permittivity and Permeability?

Solution:. Permittivity is the ability of a material to allow electric fields to pass through, (like in capacitors) which depends upon the material being used and Permeability is the allowance of the magnetic field on various factors.

Q2: Find the Absolute Permeability (m) for a Material Having Relative Permeability as 950.

Solution: As we know that m-zero = 1.257 * 10^-7

and mr = 950 (given)

So, m = mr * m-zero

= 950×1.257 * 10^-7

m = 1.19415* 10^- 4 Henries/ meter