# What is Hysteresis loop ? | Retentivity and Coercivity in Hysteresis loop | Important Facts

## Contents:

• Introduction
• Magnetic Hysteresis
• Hysteresis loop definition
• Hysteresis Meaning
• A Simple Hysteresis Loop
• Hysteresis Loop with Different Parameters
• Explanation of Hysteresis Curve
• Permeability of free space
• Intensity of magnetization
• What is Magnetic Intensity?
• What is magnetic susceptibility?
• The relation between B and H
• Retentivity and Coercivity in Hysteresis loop
• Residual Magnetism
• Coercive Force

## Hysteresis loop definition

Magnetic hysteresis is a common phenomenon if a magnetic material is magnetized and completing one full cycle of magnetization. When the magnetic flux density or magnetization density (B) is plotted against the magnetic intensity of the magnetizing field (H) for one complete cycle of magnetization and demagnetization, then the resulting loop obtained is known as a hysteresis loop. The curve of the hysteresis loop can be different in shape and size dependent on the nature of the material.

## Hysteresis Meaning

This is originated from the Greek word “Hysterein”, the word Hysteresis has been derived that means lagging behind.

## Explanation of Hysteresis Curve

• When the intensity of magnetizing field (H) is increased, the magnetic flux density of the material (B) also increases as more and more domains are aligned in the direction of the externally applied magnetic field. This part is shown in the above figure as we can observe from the starting point till point “a”.
• When all the domains are aligned due to the increasing external field, the material gets magnetically saturated, i.e. the phenomenon of saturation occurs. Beyond this, if magnetic intensity (H) is increased, magnetic flux density (B) does not change, it remains the same as we can notice in the figure that after reaching point “a”, B becomes constant.
• Now, if magnetic intensity (H) is decreased, magnetic flux density (B) also decreases, but it lags behind magnetic intensity (H). Hence, we can notice in the figure that when magnetic intensity (H) becomes zero at point “b”, magnetic flux density (B) does not reduce to zero. The value of magnetic flux density (B) is retained by the material when magnetic intensity (H) is equal to ‘0’ is acknowledged as ‘retentivity’.
• Further, if the external magnetic field’s direction is reversed and the magnitude of magnetic intensity (H) is increased, the material starts demagnetizing. The observation at point “c”, the magnetic flux density (B) turn out to be ‘0’. This value of magnetic intensity (H) which is needed to reduce the magnetic flux density (B) to zero is called ‘coercivity’.
• Now, as the magnetizing field applied in the reverse direction is increased further, the material again becomes saturated but in the opposite direction as seen in the diagram at point “d”.
• When this reverse magnetizing field is reduced, magnetic flux density (B) again lags behind magnetic intensity (H), and at point “e”, magnetic intensity (H) becomes zero, but magnetic flux density (B) does not reduce to zero.
• Again when the current magnetic field direction is reversed, and magnetic intensity (H) is again increased from zero, the cycle repeats itself.

The area enclosed by the loop represents the energy loss during a complete cycle of magnetization and demagnetization.

## Permeability of free space

The permeability of free space, μo, is a constant parameter represented by an exact value of 4π x 10-7 H/m is used for air. This constant μo appears in Maxwell’s equations, which describe and relates the electric and magnetic fields along with the properties of electromagnetic radiation, i.e. it helps to relate and define quantities such as permeability, magnetization density, Magnetic intensity etc.

Magnetic Hysteresis has been discussed in this article in detail. but in addition to that, we need to clear few concept related to magnetization such as permeability, retentivity in free space and in different medium.

## Intensity of magnetization

Magnetic material in a magnetic field generates an induced dipole moment in that material, and this moment per unit volume is recognized as intensity of magnetization (I) or magnetization density.

Where   is the net induced dipole moment. Its Unit is Am-1

## What is Magnetic Intensity?

To magnetize a magnetic material, a magnetic field has to be applied. The ratio of this magnetizing field to the permeability of free space is known as magnetic intensity H.

Where , the external magnetic field is also called as the magnetic flux density.

The unit of magnetic intensity is Am-1 same as that of the intensity of magnetization.

## What is magnetic susceptibility?

The ratio of the magnitude of intensity of magnetization to that of magnetic intensity is known as magnetic susceptibility (). Magnetic susceptibility can be explained as the amount of ease with which a magnetic material can be magnetized. Hence a material with a higher value of magnetic susceptibility will be more easily magnetized compared to the others having less value of magnetic susceptibility.

=   where the symbols have their usual meanings.

Magnetic susceptibility is a scalar quantity and with no dimension, hence, no unit.

## What is magnetic permeability?

Magnetic permeability is the ratio of the value of the net magnetic field inside a material to that of the value of magnetic intensity. Here the net magnetic field inside the material is a vector addition of the applied magnetic field and the magnetic field for the magnetization of that matter. Magnetic permeability can be simply explained as the measure of the extent to which a magnetizing field can penetrate (permeate) a given magnetic material.

=

Magnetic permeability is a scalar quantity, and its unit is

Another term associated with magnetic permeability is relative permeability which can be defined as the ratio of permeability of a medium to that of the permeability of free space.

## The relation between B and H

The total magnetic field B also called flux density is the total of magnetic field lines created inside a specified area. It is represented by the symbol B.

As magnetic intensity H which is directly proportional to the external magnetic field, hence, it can be stated that magnetic field strength or magnetic intensity H can be increased by increasing either the magnitude of current or the number of turns of the coil in which the magnetic material is kept.

We know that B = μH or B = H

μr does not have a constant value rather it depends on the intensity of the field, therefore for magnetic materials, the ratio of the flux density or total magnetic field to the magnetic field strength or the magnetic intensity known by B/H.

Hence we get a non-linear curve when we plot Magnetic flux (B) and Magnetic intensity (H) in X-axis and Y-axis, respectively. But for coils with no material inside, i.e. the magnetic flux is not induced inside any material but is induced in vacuum or in case of any non-magnetic material core such as woods, plastics, etc.

We can observe that the flux density for the above materials, i.e. iron and steel becomes constant with increasing amounts of magnetic field intensity and this is known as saturation as the magnetic flux density saturates for higher values of magnetic intensity. When the magnetic intensity is low and, hence, the applied magnetics force is low, only a few atoms in the material get aligned. With the increasing magnetic intensity, the rest are also easily aligned.

However, with increasing H, as more and more flux gets crowded in the same cross-sectional area of the ferromagnetic material, very few atoms are available within that material to get aligned; therefore if we increase the H, the magnetic flux (B) does not increase any further and hence gets saturated. As mentioned earlier, the phenomenon saturation is limited to iron-core electromagnets.

## Retentivity

The retentively of a material is a measure of the amount of magnetic field remaining in the material when the external magnetizing field is removed. It can also be defined as the ability of a material to retain some of its magnetism even after the magnetization process has been stopped. Retentively depends on the materials characteristics.

After a magnetic material is magnetized some of the electrons in the atoms remains aligned in the direction of the original magnetizing field direction and behaves as tiny magnets with their own dipole moments and do not return to a completely random pattern as the rest of them does. Because of this, some amount of magnetic field or general magnetism is left within the materials. Ferromagnetic materials have comparatively high retentivity compared to other magnetizing materials making them perfect for constructing permanent magnets.

## Residual Magnetism

Residual magnetism is the amount of the magnetic flux density that can be retained by a magnetic material, and the ability to retain it is known as Retentivity of the material.

## Coercive Force

Coercive force can be defined as the amount of the magnetizing force required to eliminate the residual magnetism retained by a material.

In the further sections, we will discuss types of magnets, permanent magnets and electromagnets based on the property and nature of the materials.