PPT No. 23
* Hysteresis
* Properties of B and H
* Relation between B, M and H
Hysteresis
The plot of Magnetization M or Magnetic field B
as a function of Magnetic Field Intensity H
(i.e. M-H or B-H graph) gives the Hysteresis curve.
The permeability μ of a ferromagnetic material
can vary through the entire range of possible values
from zero to infinity and
may be either positive or negative.
Hysteresis
Hysteresis, in general, is defined as
the lag in a variable property of a system
with respect to the effect producing it
as this effect varies.
In ferromagnetic materials
the magnetic flux density B lags behind
the changing external Magnetizing field Intensity H.
Hysteresis curve is drawn by plotting the graph of
B-field vs H (or M-H) by taking the material through
a complete cycle of H values as follows
Hysteresis
Fig. Typical B-H graph (Hysteresis curve) of a ferromagnetic material
Hysteresis
First, consider an unmagnetized sample
of ferromagnetic material.
The magnetic field intensity H is initially zero at O.
H is increased monotonically,
then magnetic induction B increases nonlinearly
along the curve (OACDE)
called as the magnetization curve.
At point E almost all of the magnetic domains
are aligned parallel with the magnetic field.
Hysteresis
An additional increase in H
does not produce any increase in B.
E is called as the point of magnetic saturation of the material.
Values of permeability derived from the formula
along the curve are always positive and
show a wide range of values.
The maximum permeability as large as
occurs at the ``knee'' (point D) of the curve
Hysteresis
Next H is decreased
till it reduces to zero.
B reduces from its saturation value at "E"
to that at point "F".
Some of the magnetic domains lose their alignment
but some maintain alignment i.e.
Some magnetic flux density B
is still retained in the material
Hysteresis
The curve for decreasing values of H
(i.e. Demagnetization curve EF)
is offset by an amount FO
from that for increasing values of H
(i.e. Magnetization curve OE).
The amount of offset “FO”
is called the retentivity or
the remanence or
the level of residual magnetism.
Hysteresis
As H is increased to large values
in the negative direction,
B reaches saturation but
in the opposite direction at point "I ".
Almost all of the magnetic domains
are aligned in opposite direction
to that at point E of positive saturation.
H is varied from its maximum negative value to zero.
Then B reaches point "J."
This point shows residual magnetism
equal to that achieved for positive values of H
(OF =OJ)
Hysteresis
H is increased back
from zero to maximum in the positive direction.
Then B reaches zero value at “K” i.e.
it does not pass through the origin of the graph.
OK indicates the amount of field H required to nullify
theresidual magnetism OJ
retained in the opposite direction.
H is increased from point “K” further
in the positive direction,
then again the saturation of B is reached at point “E”
and the loop is completed.
Hysteresis
The magnetization curve is not retraceable.
The domains forced to coalesce into large domains
aligned with the external field
maintain the alignment
and retain magnetism
even after the external field is removed.
The state of a system depends on
the history of its state.
Hysteresis
The state (value and direction) of B depends upon
the previous state of H
(value=zero/ +ve/ -ve and
direction increasing/ decreasing).
Ferromagnetic materials have
"memory" of previous exposure
to magnetism or magnetic history.
This phenomenon is called as Hysteresis.
Hysteresis
The curve for decreasing values of H
(i.e. Demagnetization curve EF)
is offset by an amount FO
from that for increasing values of H
(i.e. Magnetization curve OE).
The amount of offset “FO”
is called the retentivity or
the remanence or
the level of residual magnetism.
Hysteresis
This property has been used to advantage
in magnetic memory devices e.g.
recording of audio tape/ video tape,
and the magnetic storage of data on computer disks.
From the hysteresis loop,
important magnetic properties
of a material can be determined as follows
Hysteresis
1.Retentivity A measure of the residual flux density corresponding to
the saturation of a magnetic material.
It is a material's ability to retain
a certain amount of residual magnetic field
when the magnetizing force
is removed after achieving saturation
(The value of B at point E on the hysteresis curve).
Hysteresis
2. Residual Magnetism or Residual Flux The magnetic flux density B that remains in a material
when the magnetizing field intensity H is zero.
Residual magnetism and retentivity are same
only when the material is magnetized
to the saturation point.
However, it may be lower than
the retentivity value otherwise.
Hysteresis
3. Coercive Force or Coercivity
It is the amount of reverse magnetizing field intensity
which must be applied to a magnetic material
to make the magnetic flux density of ferromagnetic material
return to zero after it has reached saturation.
(The value of H at point G on the hysteresis curve).
Hysteresis
4. Reluctance It is the opposition
that a ferromagnetic material shows
to the establishment of a magnetic field.
Reluctance is analogous to
the resistance in an electrical circuit
Hysteresis
5.Permeability, μPermeability is the property of a material
that measures the ease with which
a magnetic flux is established in it.
μ is negative in the II and IV quadrants and
positive in the I and III quadrants of
the B-H graph (i.e. the Hysteresis curve).
Hysteresis
The curve for decreasing values of H
(i.e. Demagnetization curve EF) is offset by an amount FO
from that for increasing values of H
(i.e. Magnetization curve OE).
The amount of offset “FO” is called the retentivity or
the remanence or the level of residual magnetism.
Hysteresis
The knowledge of these properties of materials
is useful for selecting materials
appropriate for different applications e.g.
Materials having both a large remanence and
a large coercivity are selected for
designing a permanent magnet.
Materials possessing small remanence and
small coercivity are selected for
making transformer circuits.
Relation between B, M and H
Consider a general medium made up of
molecules which are polarizable and
possesses a net magnetic moment
(i.e. magnetizable).
Any circulation in the magnetization Mr produces
an effective magnetization volume current density jm
in the medium given by
Relation between B, M and H
jm is usually distinguished from
the true (real) current density, Jt.
Jt represents the flow of free charges in the medium.
The free current may be flowing through the wires
in the magnetized material or
through the material itself,
if it is a conductor.
Relation between B, M and H
In addition there is a third type of current due to
the accumulation of bound charges within
the polarizable medium called as polarization current.
The polarization current density, jp, is given by
Thus, the total current density, j,
in the medium is the sum of three real physical currents
Relation between B, M and H
Here only the I term jt is due to the motion of real charges
(over more than atomic dimensions).
Ampère's law in vacuum (differential form) is given by
Using the above expression for total current density jt
and the definition of displacement vector
equation of Ampere’s law can be written as
Relation between B, M and H
Rearranging the above equation becomes
(H = Magnetic field intensity)
This equation is the general form of Ampere’s law
applicable in vacuum and in a medium as well.
The relation between three magnetic vectors B, M, H
can also be expressed in SI units as
Ampere’s law for magnetized materialsDifferential form
H has the same dimensions as Magnetization M
(i.e., magnetic dipole moment per unit volume).
In a steady-state current situation the above equation
(in the form of Curl of H) becomes
This is the Ampere’s law for magnetized materials
in Differential form
Ampere’s law for magnetized materials
in Integral form
Differential form Ampere’s law for magnetized materials
can be converted to Integral form by Stokes' theorem as
The line integral of H around some closed curve C
is equal to IFree
(Total free current passing through the Amperian loop)
or the flux of true current density jt
through any surface S enclosed by that curve.
Properties of B and H
In isotropic materials M is proportional to B, then
the relationship between B and H is written as
B = μ H or
H = B/μ, (where μ = permeability of the material).
H = B/μ0 for free space
(as there is no magnetization, M, in free space).
H field is due to free currents while
B field is due to free and bound currents both.
Properties of B and H
∇· B = 0
(Divergence of B is zero
as Free magnetic charges do not exist)
−∇· μ0M = ρb
ρb = Bound magnetic charge density
(by the definition of M)
Properties of B and H
Field lines of B form closed loops as
∇· B =0.
But the field lines of H
begin and end on magnetic charges /
flow in both directions from magnetic poles
(as per Gilbert’s magnetic pole model) where
∇· M is not equal to zero as
∇·H= -∇·M
Properties of B and H
Ampere’s Law in vacuum
is expressed in terms of B
Ampere’s law in magnetized materials
Is expressed in terms of H
H represents how a magnetic B-field affects
the organization of magnetic dipoles
in a given material.
Properties of B and H
Though H is an auxiliary quantity derived from B-Field,
H is more familiarly known and
more often used in laboratory experiments than B.
H is the (free) current flowing in wires and
read directly in meters.
B depends upon the type and
also the magnetic history of materials.
Properties of B and H
Magnetization M in magnetic field
is analogues to Polarization P
of dielectric materials in electric field.
Magnetic field intensity H
in Magnetostatics is analogues to
electric displacement vector D
in Electrostatics.
Magnetic flux density B
is analogues to electric field intensity E.
The Three Magnetic Vectors
Out of the three magnetic vectors B, M and H,
the magnetic field B specifies the force acting
on a charge q moving with velocity v as
The Magnetization M denotes
the magnetic dipole moment per unit volume.
The magnetic intensity H
has no clear physical meaning.
Properties of B and H
The advantage for introducing H is that
H is determined by the real current density
which can be controlled directly
and measured easily.
If the constitutive relation connecting B and H is known,
then fields in the presence of magnetic materials
can be calculated using H
even if the distribution of magnetization currents
is not known.