# Magnetic Properties of Matter

## (1) Introduction

• All substances possess magnetic properties and most general definition of magnetism defines it as a particular form of interactions originating between moving electrically charged particles.
• Magnetic interaction relates spatially separate material objects and it is transmitted by means of magnetic field about which we have already studied .This magnetic field is important characteristics of EM form of matter.
• We already know that source of magnetic field is a moving electric charge i.e. an electric current. On atomic scale, there are two types of macroscopic current associated with electrons.
a) Orbital current is which electron in an atom moves about the nucleus in closed paths constituting electric currents loops
b) Spin currents related to the internal degrees of freedom of the motion of electrons and this can only be understood through quantum mechanics.
• Like electrons in an atom, atomic nucleus may also have magnetic properties like magnetic moment but it is fairly smaller then that of electrons.
• Magnetic moment m is nothing but the quantitative measure of the magnetism of a particle.
• For an elementary closed loop with a current i in it, the magnitude |m| of a magnetic moment vector equals the current times the loop area S i.e.
|m|=iS and direction of m can be determined using right hand rule.
• All micro structural elements of matter electrons, protons and neutrons are elementary carriers of magnetic moment and combination of these can be principle sources of magnetism
• Thus magnetic properties are inherent to all the substances i.e. they are all magnets
• An external magnetic field has an influence on these atomic orbital and spin currents and two basic effects of an external field are observed

i) First is diamagnetic effect which is consequences of faraday's law of induction. According to the Lenz law’s, a magnetic field always sets up an induced current with its magnetic field direction opposite to an initial field .Therefore diamagnetic moment created by the external field is always negative related to this field
ii) Second effect occurs if there is a resultant non zero magnetic moment in the atom i.e. there is a spin magnetic moment and orbital magnetic moment .In this case external field will attempt to orient the intrinsic atomic magnetic moment in its own direction .As a result a positive moment parallel to the field is created and this is called paramagnetic moment.

• Because of the universality of the diamagnetic effect, all substances possess diamagnetic.
• However, diamagnetism is by no means actually observed in all matter. This is because in many instances the diamagnetic effect is masked by the more powerful paramagnetic effect.
• Thus in paramagnetic substances we actually always observe a difference effect produced by the prominent Para magnetism and weaker diamagnetism.

(2) Important terms used in magnetism

## (a) Intensity of Magnetization:

• Intensity of magnetization is denoted by the letter I.
• It represents the extent to which the material is magnetized.
• When we place a material in the magnetic field, atomic dipoles of the material tends to align fully or partially in the direction of the field.
• So net magnetic moment is developed in the direction of the field in any small volume of the material.
• Intensity of magnetism is defined as the magnetic moment per unit volume of the magnetized material so,
I=M/V                      ----(1)
where M is the total magnetic moment within volume due to the magnetizing field.
• Unit of I is Am-1.

## (b) Magnetic Field strength

• When a substance is placed in external magnetic field ,the material gets magnetized
• The actual magnetic field inside the material is the sum of external field and the field due to magnetization
• Now we can define a new vector H where
H=B0 - I                      ----(2)
where B is the magnetic field induction inside the substance and I is the intensity of magnetization
• Unit of H is same as that of I i.e Am-1
• CGS unit of H is oersted
• In the absence of any material I=0 so
H=B0                      ----(3)

## (c) Magnetic Susceptibility

• Magnetic Susceptibility is a measure of how easily a substance is magnetized in a magnetic field
• For paramagnetic and diamagnetic substances ,the intensity of magnetization I is directly proportional to the magnetic intensity .Thus
IH                             ----(4)
where proportionality constant χ is known as Magnetic Susceptibility of the material
• Since H and I have unit unit so χ is a dimensionless constant and it is a pure number
• value of χ is zero in vacuum as there can no magnetization in vacuum

## (d) Magnetic permeability

• Magnetic intensity is given by

H=B0 - I
or
B0(H+I )
0(HH)
0H(1+χ)
we can also write this as
BH
where μ=μ0(1+χ) is a constant called permeability of the material
• μ0 is the permeability of vacuum as χ=0 for vacuum
• The constant
μr=μ/μ0=1+χ
is called the relative permeability of the material