Energy Loss Due to Hysteresis in Magnetic Materials
Energy loss due to hysteresis
•
According to
Ewing's theory
of molecular
magnetism, a
magnetic material
even in the
unmagnetised condition
.
•
It consists of an
indefinitely large number
of
molecular magnets
endowed (
provide
) with
definite polarity.
•
When a
magnetizing field
is applied, the
molecular magnets
align
themselves in the
direction of the field.
•
During this process,
work is done
by the
magnetizing field
in turning the molecular
magnets against the
mutual attractive forces
.
•
This
energy
required to
magnetize
a specimen
is
not completely recovered
when the
magnetizing field is
turned off,
since the
magnetization does not become
zero
.
•
The
specimen
retains some
magnetization
because some of the
molecular magnets
remain
aligned in the new formation due to the
group forces
.
•
To
tear
them out completely, a
coercive force
in
the
reverse direction
has to be applied.
•
Thus, there is a
loss of energy
in taking a
ferromagnetic material
through a
cycle of
magnetization.
•
This
loss of energy
is called
hysteresis loss
and
appears in the form of
heat
.
•
Consider a
magnetic material
having n
molecular magnets
per unit volume.
•
Let
m
be the
magnetic moment
of
each magnet
and
θ
the
angle
which its
axis
makes with the
direction of
magnetizing field
H
.
•
The
magnetic moment
m
of the
molecular magnet
can be resolved into a component
m cos
θ
in the
direction
of
H
and
m sin
θ
perpendicular
to
H
.
•
The component
m cos
θ
alone contributes to the
magnetising field
and the component
m sin
θ
has
no effect on the magnetisation of the specimen.
•
If
M
be the
intensity of magnetisation
, then
•
M = ∑ m cos
θ
……….. (1)
•
Differenting
Eq. (1),
•
dM = d (∑m cos
θ
) = - ∑m sin
θ
d
θ
. ... (2)
•
When
M
increases
to
M + dm
,
θ
decreases to
θ
-
d
θ
.
•
The work done by the field in decreasing
θ
by
d
θ
is
given by
•
dW = C(-d
θ
)
………(3)
•
Hence,
C
=
torque for unit deflection
= µ
o
mHsin
θ
•
dW
=
µ
o
mHsin
θ
х
(-d
θ
)
= - µ
o
mHsin
θ
d
θ
•
The work done by the applied field is
•
= ∑dW = µ
o
H
х
(-∑m sin
θ
d
θ
)
•
= µ
o
H
х
dM
•
Thus work done by the magnetizing field per unit
volume of the material for completing a cycle is,
•
W =
•
Now,
B
=
µ
o
(H + M
), for ferromagnetics , M>>H.
•
So
B
=
µ
o
M
•
i.e., dB = µ
o
dM…..(6)
•
From eq. 5 & 6
•
W =
•
The area of the
B - H
loop or
µ
o
times the area
of the
M – H
loops gives the energy spent per
cycle.
•
When
H
is in
Am
-1
and
B
is in
Wb m
-2
, the
energy is in
joules per cycle per m
3
of the
material.
In the realm of magnetism, magnetic materials exhibit unique behavior even when not magnetized. Ewing's theory sheds light on the alignment of molecular magnets in relation to an applied magnetizing field, resulting in energy consumption. This leads to hysteresis loss, where energy is dissipated as heat due to cyclic magnetization processes. The process involves aligning molecular magnets against attractive forces, necessitating a coercive force for complete demagnetization. Through mathematical derivations, the work done by the magnetizing field can be quantified per unit volume of material for a complete cycle.
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Presentation Transcript
According magnetism, a magnetic material even in the unmagnetised condition. It consists of an indefinitely large number of molecular magnets endowed (provide) with definite polarity. When a magnetizing field is applied, the molecular magnets align themselves in the direction of the field. to Ewing's theory of molecular
During this process, work is done by the magnetizing field in turning the molecular magnets against the mutual attractive forces. This energy required to magnetize a specimen is not completely magnetizing field is turned off, since the magnetization does not become zero. The specimen retains some magnetization because some of the molecular magnets remain aligned in the new formation due to the group forces. recovered when the
To tear them out completely, a coercive force in the reverse direction has to be applied. Thus, there is a loss of energy in taking a ferromagnetic material through a cycle of magnetization. This loss of energy is called hysteresis loss and appears in the form of heat. Consider a magnetic molecular magnets material per having volume. n unit
Let m be the magnetic moment of each magnet and the angle which its axis makes with the direction of magnetizing field H. The magnetic moment m of the molecular magnet can be resolved into a component m cos in the direction of H and m sin perpendicular to H. The component m cos alone contributes to the magnetising field and the component m sin has no effect on the magnetisation of the specimen. If M be the intensity of magnetisation, then M = m cos .. (1)
Differenting Eq. (1), dM = d ( m cos ) = - m sin d . ... (2) When M increases to M + dm, decreases to - d . The work done by the field in decreasing by d is given by dW = C(-d ) (3) Hence, C = torque for unit deflection = omHsin dW = omHsin (-d ) = - omHsin d The work done by the applied field is = dW = oH (- m sin d ) = oH dM
Thus work done by the magnetizing field per unit volume of the material for completing a cycle is, W = Now, B = o(H + M), for ferromagnetics , M>>H. So B = oM i.e., dB = odM ..(6) From eq. 5 & 6 W =
The area of the B - H loop or otimes the area of the M H loops gives the energy spent per cycle. When H is in Am-1and B is in Wb m-2, the energy is in joules per cycle per m3of the material.
