field is a force which is generated due to energy change in a volume of space.
magnetic field is produced by an electrical charge in motion e.g. current
flowing in a conductor, orbital movement and spin of electrons.
magnetic field can be described by imaginary lines as shown in the figure below
for a magnet and a current loop.
Magnetic field Strength
a magnetic field, H, is generated by a cylindrical coil
(solenoid) of n turns and length l, H = nI/l (A/m)
ØMagnetic flux density, B: It is the magnitude of the
field strength within a substance subjected to a field H B = H
(Tesla or Weber/m2)
called the permeability, is the measure of
the degree to which a material can be magnetized.
vacuum B = oH. o is the
permeability of vacuum and is a universal constant. o = 4 x 10-7(H/m).
r = /o is the relative
a moving charge, electrons produce a small magnetic field having a magnetic
moment along the axis of rotation.
spin of electrons also produces a magnetic moment along the spin axis.
in a material arises due to alignment of magnetic moments.
Magnetic Dipole and Monopole
to electric dipole, a magnetic dipole can be
defined as two monopoles of opposite and equal
strength separated by a certain distance.
magnetic monopole, however, is not observed in nature.
there are N monopoles each located at a point given by a vector ā,
then the magnetic dipole moment can be defined as a vector, ū N u mai i
monopoles of strength +m and –m separated by distance l, will
give a dipole ū = mā1 – mā2 = m(ā1
– ā2) = mĪ
bar magnet can be thought of consisting of two opposite and equal poles at its
the application of a magnetic field magnetic moments in a material tend to
align and thus increase the magnitude of the field
increase is given by the parameter called magnetization, M, such that B = oH + oM.
M = mH.
is called magnetic susceptibility.
= r – 1
on the existence and alignment of magnetic moments with or without application
of magnetic field, three types of magnetism can be defined.
Ø Diamagnetism is a weak form of magnetism which arises
only when an external field is applied.
arises due to change in the orbital motion of electrons on application of a
is no magnetic dipoles in the absence of a magnetic field and when a magnetic
field is applied the dipole moments are aligned opposite to field direction.
magnetic susceptibility, m
(r – 1) is negative
i.e. B in a diamagnetic material is less than that of vacuum.
H =0 H
Al2O3, Cu, Au, Si, Zn
a paramagnetic material the cancellation of magnetic moments between electron
pairs is incomplete and hence magnetic moments exist without any external
the magnetic moments are randomly aligned and hence no net magnetization without
any external field.
a magnetic field is applied all the dipole moments are aligned in the direction
of the field.
magnetic susceptibility is small but positive. i.e. B in a paramagnetic
material is slightly greater than that of vacuum.
Paramagnetic materials: Al, Cr, Mo, Ti, Zr
materials posses permanent magnetic moments in the absence of an external
magnetic field. This is known as ferromagnetism.
magnetic moments in ferromagnetic materials arise due to uncancelled electron
spins by virtue of their electron structure.
coupling interactions of electron spins of adjacent atoms cause alignment of
moments with one another.
origin of this coupling is attributed to the electron structure. Ferromagnetic
materials like Fe (26 – [Ar] 4s23d6) have incompletely
filled d orbitals and hence unpaired electron spins.
the coupling of electron spins results in anti parallel alignment then spins
will cancel each other and no net magnetic moment will arise.
is known as antiferromagnetism. MnO is one such example.
MnO, O2- ions have no net magnetic moments and the spin moments of
Mn2+ ions are aligned anti parallel to each other in adjacent atoms.
ionic solids having a general formula MFe2O4, where
M is any metal, show permanent magnetism, termed
ferrimagnetism, due to partial cancellation of spin moments.
Fe3O4, Fe ions can exist in both 2+ and 3+ states as
in 1:2 ratio. The antiparallel coupling between Fe3+ (Half in
A sites and half in B) moments cancels each other. Fe2+ moments are
aligned in same direction and result in a net magnetic moment.
materials exhibit small-volume regions in which magnetic moments are aligned in
the same directions. These regions are called domains.
domains are separated by domain boundaries. The direction of magnetization
changes across the boundaries.
magnitude of magnetization in the material is vector sum of magnetization of
all the domains.
Magnetization and Saturation
ØWhen a magnetic field is applied to a ferromagnetic material,
domains tend to align in the direction of the field by domain boundary movement
and hence, the flux density or magnetization increases.
ØAs the field strength increases
domains which are favorably oriented to field direction grow at the expense of
the unfavorably oriented ones. All the domains are aligned to the field
direction at high field strengths and the material reaches the saturation
slope of the B-H curve at H =0 is called initial permeability, i, which is a material
the field is reduced from saturation by magnetic reversal, a hysteresis
the field is reversed the favorably oriented domains tend to align in the new
direction. When H reaches zero some of the domains still remain aligned
in the previous direction giving rise to a residual magnetization called
Hc, the reverse filed strength at which
magnetization is zero, is called Coercivity
Hard and Soft magnets
on their hysteresis characteristics ferro and ferrimagnetic materials can be
classified as hard and soft magnets.
Ø Soft magnets have a narrow hysteresis curve and high
initial permeability and hence easy to magnetize and demagnetize. It is just
opposite for the Hard magnets.
Hard and Soft magnets
magnetic hardness is expresses by a term called energy
product which is the area of the largest rectangle that can be drawn in
the second quadrant (red-hatched).
ØConventional hard magnetic materials like steel,
Cunife(CuNi-Fe) alloys, Alnico (Al-Ni-Co) alloy have BHmax values in
the range of 2 – 80 kJ/m3. High-energy hard
magnetic materials like Nd2Fe14B, SmCo5 exhibit
80 kJ/m3. ØHard
magnets are used in all permanent magnets in applications such as power drills,
magnets like Fe, Fe-Si are useful when rapid magnetization and demagnetization
is required as in transformer cores.
and other defects should be low for this purpose as they may hinder the domain
wall movement through which domains align.
magnetic properties of a crystalline material are not isotropic i.e. properties
are not the same in all crystallographic direction.
always happens to be a preferred direction in which magnetization is easier.
For example,  direction is the preferred magnetization direction in Co.
For Fe it is  as shown in the diagrams below.
Effect of Temperature
atomic vibration increases with increasing temperature and this leads to
misalignment of magnetic moments. Above a certain temperature all the moments
are misaligned and the magnetism is lost. This temperature is known as Curie
and ferrimagnetic materials turn paramagnetic above curie point. For Fe Tc =
768 C, Co
– 1120 C,
Ni – 335 C.
Below Tc Above
Tc Temperature Tc
ØSuperconductivity is disappearance of electrical
resistance below a certain temperature.
temperature below which superconductivity is attained is known as the critical temperature, TC.
superconducting behavior is represented in a graphical form in the figure
Bardeen-Cooper-Schreiffer (BCS) Theory
ØJohn Bardeen, Leon
Cooper and John Schreiffer – BCS theory, Noble prize for Physics in 1972
temperature dependence of metals arises out of scattering of electrons due to
atomic vibrations which increase with temperature.
ØCooper pair – Below TC two electrons
can pair through the lattice phonon which causes a slight increase in the
positive charge around an electron and since thermal energy to scatter is low,
this pair can move through the lattice.
Motion of Cooper pair
through the lattice
BCS Theory contd..
ØThus the charge
carrier in a superconductor is a pair of electrons instead of a single
theory applies well to conventional superconductors like Al (TC =
1.18 K), Nb3Ge (TC = 23 K).
ØHigh temp. superconductors – Recently a number of
ceramic superconductors such as YBa2Cu3O7 have
been discovered whose TC is much higher.
Superconductivity and Magnetism
material in its superconducting state will expell all of an applied magnetic
field (Fig. b). This is Meisnner effect.
magnet placed over a superconductor will thus float, a phenomenon known as magnetic levitation.
(a) T>TC (b) T<TC
Messner effect. (a)
Above TC , normal conducting state, magnetic flux penetrates. (b)
below TC, superconducting, the magnetic field is expelled.
Types of Superconductors
the field is increased, some of the superconducting materials come back to
normal conducting state above a critical magnetic field HC (Fig. c)
– These are Type I superconductors. Ex. Al , Pb
class of materials the field begins to intrude above a critical value of the
applied field (HC1) and at a higher field (HC2) it turns
into a normal conductor (Fig. d). The transition is gradual here unlike Type I.
These are called Type II superconductors.