Parameters of Magnetic Materials

PARAMETERS OF MAGNETIC MATERIALS

1. Magnetic dipole moment (M_μ)

A system having two opposite magnetic poles separated by a distance 'd' is called as a magnetic dipole. If 'm' is magnetic pole strength and 'l' is the length of the magnet, then its dipole moment is given by

Mμ = ml

Magnetic moment can also be defined as M_μ=ia, where i is the electric current that flows through a circular wire of an area of cross section 'a'.

2. Bohr Magneton

The orbital magnetic moment and the spin magnetic moment of an electron in an atom can be expressed in terms of smallest atomic unit of magnetic moment called Bohr magneton.

1 Bohr Magneton = e/2m

⇒ μ_B =  9.27 × 10⁻²⁴ Am²

3. Magnetic field

The space around the magnet (or) the current carrying conductor where the magnetic effect is felt is called Magnetic field.

4. Magnetic lines of force

Magnetic field is assumed to consist of lines of magnetic forces. These lines of forces travels externally from north pole to south pole as shown in Fig. 1.1. Hence a magnetic line of force is defined as the continuous curve in a magnetic field. The tangent drawn at any point on the curve gives the direction of the resultant magnetic intensity at that point.

5. Magnetic lines of induction

The magnetic lines of force which originates from north pole to south pole doesn't end there itself. They are supposed to continue through the magnet and reach the north pole from where they started and forms a closed loop as shown in Fig. 1.2. Such imaginary lines are called magnetic lines of induction.

6. Forces between two poles

Let us consider two poles of pole strength m₁ and m₂ placed at a distance 'r' apart as shown in Fig. 1.3.

From the coulomb's law of forces, the force of attraction (or) repulsion between the isolated point magnetic poles is proportional to the product of pole strengths and is inversely proportional to the square of the distance between them.

(i.e.,) 

Interms of unit vector  directed from m₁ to m₂

=r/

Here K is a constant of proportionality.

where μ₀ → Permeability in free space (4π × 10^‒7 H/m.)

μ_r → Relative Permeability

For air μ_r = 1

7. Magnetic induction (or) Magnetic flux density (B)

It is defined as the number of magnetic lines of force passing normally through unit area of cross section A at that point as shown Fig. (1.4)

i.e., 

8. Magnetic field intensity (H)

It is defined as the force experienced by a unit north pole placed at the given point in a magnetic field.

9. Magnetisation (or) Intensity of magnetisation [M (or) I]

The term magnetisation is the process of converting a non magnetic material into a magnetic material. It measures the magnetisation of the magnetised specimen.

It is also defined as the magnetic moment per unit volume.

M = M_μ / V = m.l  /  l.a = m/a weber/m²

10. Magnetic Susceptibility (χ_m)

It is the measure of the ease with which the specimen can be magnetised by the magnetising force.

It is defined as the ratio between intensity of magnetisation (I) and the magnetic field intensity (H)

(i.e.,) χ_m = I / H

11. Magnetic Permeability (μ)

It is defined as the ratio between the magnetic flux density (B) and the magnetic field intensity (H)

  μ = μ₀μ_r = B / H

It is the measure of degree at which the lines of force can penetrate through the material.

12. Relative Permeability (μ_r)

It is the ratio between the permeability of the medium to the permeability of free space.

 μ_r = μ/μ₀

13. Relation between μ_r and χ_m

When a magnetic material is placed in a magnetic field (H), then two types of lines of induction passes through the material. viz.,

 (i) Due to magnetising field (H)

 (ii) Due to material itself being magnetised by induction (I)

  ∴ Total flux density B = μ₀ (H+I)        ...(1)

We know, μ = B/H ⇒ B = μH           …….(2)

Equating equation (1) and (2) we get

μH = μ₀ (H+ I)

Since μ=μ₀μ_r, we have

 μ₀μ_rН = μ₀H( 1+ I/H )

Here 1/H = χ_m

 μ_r = ( 1+ 1/H ) = 1 + χ_m

μ = 1+χ_m

14. Retentivity (or) Remanence (M_r)

When the external magnetic field applied to a magnetic material is removed, the magnetic material will not loss its magnetic property immediately. There exits some residual intensity of magnetisation in the specimen even when the magnetic field is cut off. This is called residual magnetism or retentivity.

15. Coercivity (‒H_C)

The residual magnetism can be completely removed from the malarial by applying a reverse magnetic field. Hence Coercivity of the magnetic material is the strength of reverse magnetic field (‒H_c) which is used to completely demagnetise the material.