Magnetic moment of a current loop:

Magnetic moment of a current carrying circular loop is given by:

M = I A

where M = magnetic moment of a current loop, I = current through loop, A = area of loop.

Magnetic dipole moment:

Magnetic dipole moment M is analogous to electric dipole moment P.

Circular current loop as a magnetic dipole:

The magnetic flux density on the axis of circular current loop at the distance ‘x’ from the centre of loop is given by (assuming that radius ‘a’ of loop is much smaller than distance ‘x’):

B = (μ₀/4π) × (2M/x³)

where B = magnetic flux density on the axis of current carrying circular loop at the distance of ‘x’ from the center of loop, μ₀ = permeability of free space = 4π × 10^-7 H/m, M = magnetic dipole moment = I A, I = current through loop, A = area of loop.

Magnetic dipole moment of a revolving electron:

Magnetic dipole moment of a revolving electron is given by:

M₀ = e v r / 2 = (e/2m) L₀

where M₀ = magnetic dipole moment of a revolving electron, e = charge on electron, v = velocity of electron, r = radius of orbit, m = mass of electron, L₀ = angular momentum of electron. If electron’s orbit is in the plane of paper and electron is moving in anticlockwise direction, then it gives rise to conventional current in clockwise direction, and direction of magnetic dipole moment is perpendicular to plane of paper and going into the paper. Vectors M₀ and L₀ are oppositely directed.

Gyromagnetic ratio of electron:

The ratio of magnetic dipole moment with angular momentum of revolving electron is called the gyromagnetic ratio. It is given by:

Gyromagnetic ratio = M₀/L₀ = e/(2m) = 8.8 × 10¹⁰ C/kg

Magntization (M_z):

The net magnetic dipole moment per unit volume is called the magnetization (M_z) of the sample.

Curie’s law:

Curie’s law states that the magnetization of a paramagnetic sample M_z is directly proportional to the external magnetic field induction and inversely proportional to the absolute temperature. This law can be expressed in terms of an equation as follows:

M_z = C B_ext / T

where C = Curie’s constant, B_ext = external magnetic flux density, T = temperature.

Magnetic field intensity (H):

Magnetic field intensity H is defined as quantity appearing in the below given equation (for free space):

B = μ₀ H

In the presence of magnetic material, above equation needs to be modified as follows:

B = μ₀ (H + M_z)

where B = magnetic flux density, μ₀ = permeability of free space = 4π × 10^-7 H/m, H = magnetic field intensity. Unit of μ₀ is H/m or henry/meter. M = magnetization of material. H and M have same unit and it is A/m or ampere/meter. Do not confuse between magnetic field intensity H and unit H (henry)

Magnetic susceptibility (χ):

Magnetic susceptibility χ of any material is defined as the ratio of magnetization of that material to magnetic field intensity of applied magnetic field. Alternatively, magnetic susceptibility is defined as the quantity appearing in the following equation:

M_z = χ H

where M_z = magnetization of the material, χ = magnetic susceptibility of the material, H = magnetic field intensity of the applied magnetic field. χ is a dimensionless quantity.

Relative magnetic permeability (μ_r):

Relative magnetic permeability of material ‘μ_r ’ is defined as follows:

μ_r = 1 + χ

where χ = magnetic susceptibility of the material. μ_r is a dimensionless quantity.

Classification of substances on the basis of magnetic properties:

On the basis of magnetic properties, substances are classified into three categories: (a) diamagnetic substances, (b) paramagnetic substances, and (c) ferromagnetic substances.

Diamagnetic substances:

Substances which are weakly repelled by a magnet are called diamag- netic substances. In diamagnetic substance, magnetic dipole moments of all the electrons in atom cancel each other and resulting magnetic moment of the atom is zero. For diamagnetic substances, magnetic susceptibility is negative. Diamagnetism is universal and present in all materials. But it is weak and hence hard to detect if material is paramagnetic or ferromagnetic.

Properties of diamagnetic substances:

Properties of diamagnetic substances are as follows:

(a) If a thin rod of a diamagnetic material is freely suspended in external magnetic field, it comes to rest with its length perpendicular to the direction of the field.

(b) If diamagnetic material is placed in an external non-uniform magnetic field, it tends to move from the stronger part of the field to the weaker part of the field.

(c) In the absence of external magnetic field, the net magnetic moment of diamagnetic substance is zero.

(d) Diamagnetic substance lose their magnetism on removal of external magnetic field.

(e) If a diamagnetic gas is introduced between the pole-pieces of a magnet, it spreads at right angles to the magnetic field.

(f) Silver, lead, silicon, nitrogen, sodium chloride, bismuth, copper, antimony, gold, mercury, water, air, hydrgen, etc. are examples of diamagnetic substances.

Paramagnetic substances:

Substances which are weakly attracted by a magnet are called paramagnetic substances. In paramagnetic substance, the magnetic dipole moments of all the electrons do not cancel out, resulting in some dipole moment for an atom so that each atom of paramagnetic substance is equivalent to tiny magnetic dipole, called atomic magnet. In the absense of external magnetic field, the dipole moments of the atoms are randomly oriented and hence the net dipole moment of the substance is zero. Magnetic susceptibility of paramagnetic substance is positive and small. When paramagnetic substance is kept in an external magnetic field, the tiny atomic magnets tend to align parallel to the applied field and show temporary magnetization. As soon as the external field is removed, the atomic magnets again get randomly oriented and magnetism is lost.

Properties of paramagnetic substances:

(a) If a thin rod of paramagnetic material is freely suspended in a uniform magnetic field, it comes to rest with its length parallel to the direction of the field.

(b) These materials when placed in an external non-uniform magnetic field, tend to move from the weaker part to the stronger part of the field.

(c) In the absence of external magnetic field, the dipole moments of the atoms are randomly oriented and hence the net dipole moment of the paramagnetic substance is zero.

(d) When paramagnetic substance is kept in an external magnetic field, the tiny atomic magnets tend to align their axes parallel to the applied field and show magnetic effects. As soon as the external field is removed, the atomic magnets again get randomly oriented and the substance loses its magnetism.

(e) Since paramagnetic substances lose their magnetism on removal of external field, they can not be used to make permanent magnets.

(f) If a paramagnetic gas is introduced between the pole pieces of a magnet, it spreads in the direction of the field.

(g) Aluminium, manganese, chromium, platinum, oxygen, sodium, calcium, lithium, tungsten, nio- bium, etc. are examples of paramagnetic substances.

(h) The magnetic susceptibility of paramagnetic material is small and positive, and it is inversely proportional to temperature of the substance.

Ferromagnetic substances:

Substances which are strongly attracted by a magnet are called ferromagnetic substances. They have positive and large magnetic susceptibility. The atoms of ferromag- netic substances acquire a high degree of magnetic alignments, even when they are placed in a weak external magnetic field. Also, they retain some magnetism even after the removal of the external field. Hence, ferromagnetic substances are used to make permanent magnets.

Properties of ferromagnetic substances:

Properties of ferromagnetic substances are as follows:

(a) These materials when placed in an external uniform magnetic field, are strongly magnetized in the direction of the external magnetic field.

(b) These materials when placed in an external non-uniform magnetic field, tend to move from the weaker part to the stronger part of the field.

(c) Atom of a ferromagnetic material has a resultant magnetic moment even in the absence of exter- nal magnetic field.

(d) When a thin rod of ferromagnetic substance is suspended freely between two conical pole pieces of an electromagnet, it comes to rest with its axis parallel to the magnetic field between the two poles.

(e) Iron, nickel, cobalt, gadolinium, etc. are examples of ferromagnetic substances.

(f) The magnetic susceptibility of a ferromagnetic material is very high and positive.

(g) Magnet made up of ferromagnetic material is called ferromagnet. Ferromagnets remain magne- tized even after the removal of the magnetic field.

Domain theory of ferromagnetism:

Domain theory was proposed by Weiss. According to this theory, a ferromagnetic material contains a large number of small regions or domains. Typical do- main size is 1 mm. Magnetic moments of all the atoms in one domain are all aligned in the same direction. Hence, each domain has resultant magnetic moment. However, magnetic moments of all domains are randomly oriented hence resultant magnetic moment of a ferromagntic substance is zero, in general. When the strong magnetic field is applied to ferromagnetic material then all the domains are rotated so that they are aligned in the direction of applied magnetic field. Domains remain so even after removal of external magnetic field; it means ferromagnetic material is now turned into a permanent magnet.

Curie temperature:

When ferromagnetic substance is heated, its magnetization decreases with temperature. At a particular temperature, its domain structure is destroyed and it looses its magnetization completely, and this temperature is called Curie temperature.