# Magnetization

## What is called Magnetization?

When a magnetic material is placed in the region of a magnetic field produced by another magnet, it acquires magnetic properties by induction. This phenomenon is called magnetization.

The extent of magnetization process of a magnetic material body depend upon following –

1. Intensity of magnetization of magnetic material getting magnetization.
2. Intensity of magnetic field of produced by magnet inducing magnetization.
3. Magnetic permeability of the medium.

### Intensity of Magnetization

The degree or extent to which a material get magnetized when placed in the magnetizing field, is called intensity of magnetization.

Intensity of magnetization is denoted by ( I ) or ( M ) . It is the property of a material which represents its effectiveness to get magnetized. Its value is given by the net dipole moment per unit volume developed in the material.

Therefore, \quad \text {Intensity of magnetization} = \text {Magnetic moment developed per unit volume}

Or, \quad M = \left ( \frac {\text {Magnetic moment}}{\text {Volume}} \right )

Let, ( m ) is the dipole moment developed in a material of volume ( V ) , length ( 2 l ) and cross sectional area ( A ) .

Then, intensity of magnetization will be –

M = \left ( \frac {m}{V} \right )

Let, ( q_m ) is the pole strength of induced magnetism.

Then, \quad m = q_m \times 2l

Therefore, \quad M = \left ( \frac {q_m \times 2l}{A \times 2l} \right )

= \left ( \frac {q_m}{A} \right )

Thus, magnetization is equal to the induced pole strength per unit area of cross section of the material.

### Intensity of Magnetizing Field

The degree or extent to which a magnetic field can magnetize another magnetic material is called intensity of magnetizing field.

Intensity of magnetizing field is denoted by ( H ) . It is the property of a magnet which represents its effectiveness to produce magnetism in other magnetic materials. This property of a magnet depends upon the magnetic permeability of the medium.

Intensity of magnetizing field ( H ) is the ratio of the magnetic field ( B_0 ) to the permeability of the free space ( \mu_0 ) .

Therefore, \quad H = \left ( \frac {B_0}{\mu_0} \right ) ……. (1)

TO BE NOTED –

The terms, Intensity of Magnetizing field and Intensity of Magnetization are associated with two different bodies of magnetic material which are in interactions.

Consider that, a body (A) is a magnet which is producing its magnetic field around itself. Another body (B) made of magnetic material is placed somewhere in this field.

Intensity of Magnetization – The body (B) will get some magnetic property. This is called magnetization of body (B). The extent of magnetization by which body (B) is get magnetized, is the property of material of the body (B). This is called the Intensity of Magnetization.

Intensity of Magnetizing Field – The body (A) is a magnet and producing its magnetic field. If more strong will be the intensity of magnetic field of body (A), the more will be the intensity of magnetization developed in the body (B). This is called the effect Intensity of magnetic field of body (A).

## Magnetic Permeability

Magnetic permeability of a medium is the ability of the medium to allow magnetic field lines through it for facilitating magnetization process.

Magnetic permeability is denoted by ( \mu ) . It is the property of medium in which the process of magnetization occur. It is the measure of effectiveness of the medium to allow magnetization.

Therefore, \quad \text {Magnetic permeability} = \left ( \frac {\text {Intensity of magnetic field}}{\text {Intensity of magnetizing field}} \right )

Or, \quad \mu = \left ( \frac {B}{H} \right ) …….. (2)

### Relative Magnetic Permeability

The ratio of magnetic field ( B ) inside a material or substance to the magnetic field in vacuum ( B_0 ) is known as relative permeability.

Therefore, \quad \text {Relative permeability of medium} = \left ( \frac {\text {Intensity of magnetic field in medium}}{\text {Intensity of magnetizing field in vacuum}} \right )

Or, \quad \mu_r = \left ( \frac {B}{B_0} \right ) …….. (3)

From equation (1), we will get –

B_0 = \mu_0 H

And from equation (2), we will get –

B = \mu H

Therefore, from equation (3), we will get –

\mu_r = \left ( \frac {B}{B_0} \right )

= \left ( \frac {\mu H}{\mu_0 H} \right )

= \left ( \frac {\mu}{\mu_0} \right )

## Magnetic Susceptibility

Susceptibility is the property of a magnetic material which shows that – “How easily the substance can be magnetized when it is placed in a magnetizing field”?

It is denoted by ( x_m ) .

Magnetic susceptibility is equal to the ratio of the intensity of magnetization ( M ) to the intensity of magnetizing field ( H ) .

Therefore, \quad \text {Magnetic susceptibility} = \left ( \frac {\text {Intensity of magnetization}}{\text {Intensity of magnetizing field}} \right )

Or, \quad x_m = \left ( \frac {M}{H} \right )

Magnetic susceptibility is a dimensionless quantity.

Relation between relative permeability ( \mu_r ) and magnetic susceptibility ( x_m ) is given by the equation –

\mu_r = ( 1 + x_m )

See numerical problems based on this article.

### Curie’s Transition Law

Curie’s law states that –

Magnetic susceptibility ( x_m ) of a paramagnetic material is inversely proportional to the absolute temperature, ( T ) of the material.

Therefore, for paramagnetic materials –

x_m = \left ( \frac {\mu_0 C}{T} \right )

Where, ( C ) is the Curie’s constant.

Susceptibility-temperature graph for different materials is shown in figure.

Magnetic susceptibility ( x_m ) of a ferromagnetic material is related to its absolute temperature ( T ) . The relation is expressed as –

x_m = \left ( \frac {C}{T - T_C} \right )

Where T_C is known as curie temperature.

Magnetic susceptibility ( x_m ) of a anti-ferromagnetic material is related to its absolute temperature as –

x_m = \left ( \frac {C}{T + T_C} \right ) .

1. Therefore, curie temperature plays a vital role in magnetism.
2. At curie temperature, a sharp change in magnetic property occurs.
3. Above curie point temperature, a ferromagnetic material starts behaving like a paramagnetic material.