BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
Hysteresis curve of a ferromagnetic sample
Apparatus
1) Two solenoid coils, (Main S and Compensating C), 2) Ferromagnetic rod, 3) Reversible key
(R), 4) Current source, 5) Magnetometer, 6) Battery, 7) Rheostat and 8) Transformer.
Purpose of the Experiment
1) To study the magnetization (M) of a ferromagnetic material due to an applied magnetic
field H and to plot the hysteresis (M vs. H) curve.
2) To calculate the retentivity and coercivity of the material from the hysteresis curve.
Basic Methodology
A ferromagnetic rod is magnetized by placing it in the magnetic field of a solenoid. The
magnetized rod causes a deflection (θ) in a magnetometer. The deflection θ is recorded as the
current in the solenoid (I) is varied over a range of positive and negative values to generate
thee full hysteresis curve.
Theory of the M-H curve:
The atomic motions in materials bequeath them with magnetic properties: when placed in
an external magnetic field, they respond by aligning themselves in such a way as to reduce
the net energy of the system. A “ferromagnet” is a material in which the atoms behave like
magnetic dipoles produced by the spins of unpaired electrons. The energy of the interaction is
governed by quantum mechanics, and it turns out that this
energy is lowered, even in the absence of an external field, if
neighbouring electron spins are aligned parallel to each other.
However in a large sample, domains form in the interior of the
material within which the dipoles align in a given direction but the
domains themselves are randomly oriented as shown in the
Random orientation of the
adjacent figure. Thus the bulk material is generally unmagnetized. domains in a ferromagnet.
In the presence of an external magnetic field, the different domain moments tend to align,
producing a net magnetization in the direction of the applied magnetic field. The
magnetization M, defined as the magnetic dipole moment per unit volume, can be measured
by observing the magnetic field produced by the magnetized material. A solenoid produces a
fairly strong and uniform magnetic field within it, which is generally used to magnetize a
ferromagnetic sample
The magnetic field of a solenoid at a point well inside it, on the axis, is given by H = nI,
where n is the number of turns per unit length of the solenoidal coil, and I is the current in the
solenoid. The specimen in the form of a cylindrical rod of length “l” and cross section “A”,
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BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
placed along the axis of the solenoid, acquires a magnetization “M” along its axis. The
magnetic dipole moment “m” of the rod is then given by : m = M(lA). The magnetic field
produced by the rod at a point along the axis a distance “r” from the centre of the rod is given
by HM = (mr)/[2π (r2 – l2/4)2] (in A/m) or BM = (μo/4π)(2mr)/[2π (r2 – l2/4)2] (in tesla)
Now the total magnetic field at that point is a combination
S
of this field, the field of the solenoid and the Earth's magnetic
HRes
HE
field. In our setup, we will offset the magnetic field of the
solenoid using a compensating coil. The apparatus is aligned
such that the axis of the rod is perpendicular to the horizontal
E
W
HM
component of the Earth’s magnetic field, HE, which is along
N
South-North direction. A magnetometer needle at “r” aligns
along the resultant magnetic field making an angle θ with HE as shown in the above figure.
Clearly,
tan θ = HM/ HE
 HM = HE tan θ.
Hence, M = (4π)[(r2 – l2/4)2/(2r lA)] HE tan θ. Thus, M α tan θ.
Also, the magnetizing field H = HM α I, the current in the solenoid.
Hence, to obtain the relationship between M and H one can observe the tan θ vs. I plot.
About Hysteresis:
Ferromagnetic materials have non-linear response, in that the magnetization produced is
not linearly proportional to the magnetizing field. Moreover, when the applied field is gradually
removed, the material does not return to its original unmagnetized state. Some magnetization
is residual. This phenomenon is known as “hysteresis”.
A typical M vs. H curve is shown in the adjacent figure. As the applied field H is increased,
domains with magnetization along the direction of the applied field grow in size (or number)
and the magnetization increases rapidly. For stronger fields, whole domains that are not
aligned along the field, change their orientation and
M
finally, all the internal spins are oriented parallel to the
applied field. The magnetization has now reached
saturation (point b) and further increase in H will not
increase M. As the applied field is reduced, the
magnetization curve traces a different path up to zero
H
applied field (point c) where the magnetization has a
residual value. This is because the domains which are
aligned with the field now tend to de-align. So even
when the applied field is zero, many domains are still
aligned, thereby retaining some net magnetic field. This value of magnetization
(corresponding to the point c is called the “retentivity”. In order to remove this magnetization,
the applied field is increased in the reverse direction (up to point d). This reverse field forces
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BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
some domains to align in the new direction to make the net field zero. The field required to
achieve this condition is called the “coercive” field or “coercivity”. Further increase in reverse
field magnetizes the sample in the opposite direction in a symmetric way and the sample
reaches saturation (point e). The loop is completed on decreasing the reverse field and then
increasing through zero in the opposite direction. Note that the tan θ vs I curve also has
similar shape due to proportionality of M and H with tan θ and I respectively.
Note that in air, B= μoH. Hence for applied field, B is also used in place of H. However, it is
more correct to use H instead of B, as inside a material H remains unchanged but B changes.
Also note that B has the SI unit W/m2 or tesla (T), whereas the SI unit of H is A/m.
About Retentivity, saturation magnetization and Coercivity :
Retentivity (Mo) is the residual magnetization left in the sample when it is magnetized by
applying an external field and when this applied field is reduced to zero.
Mo = (4π/μo)[(r2 – l2/4)2/(2r lA)] BE tan θo (A/m) where tan θo = [ IcI + IfI ]/2, points c and f refer
{ μo= 4π x10-7 H/m, BE in Goa ~ 42 μT}
to the tan θ vs. I hysteresis curve.
Saturation magnetization (Ms) is the maximum (saturation) magnetization in the sample when
the applied field is maximum and magnetization does not increase any more as all the
domains in the sample have already aligned themselves with the external field.
Ms = (4π/μo)[(r2 – l2/4)2/(2r Al)] BE tan θs (A/m) where tan θs = [ IbI + IeI ]/2, points b and e refer
{ μo= 4π x10-7 H/m, BE in Goa ~ 42 μT}
to the tan θ vs. I hysteresis curve.
Coercivity (Ho) is the external field in the reverse direction, required to reduce the residual
magnetization in the sample to zero.
Ho= nIo (A/m), where Io = [ IdI + IgI ]/2, d and g refer to points on the tan θ vs. I hysteresis
curve. {Here n is turns per meter of the solenoid coil}
Experimental set-up
S : Solenoid
C : Compensating coil
N : Magnetometer
R : Reversing key
A : Ammeter (built in the power supply)
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BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
Experimental Procedure:
1) Make the electrical connections as per the circuit diagram above.
2) Rotate the dial of the magnetometer until its 0 - 0 position is aligned with the axis of the
solenoid.
3) Rotate the wooden arm containing the solenoid, magnetometer and compensating coil,
until the magnetic pointer coincides with the 0 - 0 position. In this position the wooden arm
is along the E-W direction. The horizontal component of the Earth’s magnetic field HE
(along S-N direction) is then perpendicular to the wooden arm.
4) Note down the lengths “l” of the rod, area of cross section “A” of the rod, the distance “r” of
the centre of the magnetometer needle from the midpoint of the solenoid. To get the
number of turns /meter “n” of the solenoid S, note down the total number of turns N in the
solenoid, and divide it by its length L. These values will be required to calculate retentivity
and coercivity values. Take the value of Earth’s magnetic field HE (in Goa) to be 42 μT.
5) Now position the compensating coil C to nullify the field due to the solenoid S. For this,
pass current (say 1A) through the coils S & C. Vary the position of C along the wooden
arm until the defection of the needle is zero. The magnetic field of solenoid S is now
nullified (at the position of the magnetometer) by the magnetic field of C. (Please ensure
that while doing this, the rod is not inside the solenoid S).
6) Before starting the experiment, the given
ferromagnetic rod has to be fully demagnetized.
For this purpose, connect the circuit according to
the adjacent figure. Set the AC current to
maximum. Now gradually reduce the current to
zero using the rheostat. (Note: Maximum current
corresponds to shorting of the rheostat).
Rheostat
7) Now begin the M-H curve measurement:
a) To begin with, the current in the solenoid should be switched off.
b) Insert the demagnetized specimen rod so that its leading tip is at the edge of the
solenoid. [Note: There should be no deflection of the needle at this point. If any
deflection is observed, repeat step 6 for demagnetizing the rod].
c) Switch on the current source (whose current can be varied).
Caution: From now on, strictly follow the current monotonic variation sequence. Do not
back-track the set current. This will lead to incorrect results due to hysteresis.
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BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
d) Vary the current from 0 A. Note the deflections θ1 and θ2 of the two ends of the
magnetometer needle.
e) Change the current in steps of 0.1 A and note the deflections for each setting of
current. (No reduction of current once increased, at any stage)
f) Continue until saturation is reached (i.e. deflection does not change with increase in
the current).
g) Now start decreasing the current in steps of 0.1 A and measure the deflection angle, till
you reach zero current. Now switch off the current source.
h) Reverse the position of the reversible key R, switch on the source, and repeat the
measurement of the deflection angle by varying the current in the reverse direction
from 0 A to maximum current (saturation).
i) Once you reach saturation, start decreasing the magnitude of the current till you reach
0 A.
j) Now switch off the current source and reverse the position of the key R again.
k) Switch on the source and repeat, varying the current now from 0 A to the maximum
(i.e. saturation level). You can now switch off the current source.
8) Plot a graph of tan θ vs. current I, where θ is the average of θ1 and θ2.
9) Calculate the values of b, c, d, e, f and g from this curve.
10) Calculate the retentivity (A/m), saturation magnetic field (A/m), and coercivity (A/m) values.
Results:
1) Plot of the tan θ vs. current I.
2) The values of b, c, d, e, f and g from this curve.
3) The retentivity, saturation magnetic field, and coercivity values for the given specimen.
4) Errors in the estimation of the above three values.
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BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
General information:
1) The process of demagnetization is shown in the adjacent
figure. Due to the 50 Hz AC current, the hysteresis loop is
traced out 50 times a second. However, as the current
decreases continuously with time, each subsequent loop
becomes smaller and smaller in size till it becomes a very
small loop near the origin. Thus, the specimen has no
magnetization left after this demagnetization process.
M
Ms
Mo
Hc
H
2) The area under the hysteresis loop indicates the energy
lost in each hysteresis cycle. Thin loop (small coercive
field), means smaller amount of dissipated
energy in repeatedly reversing the
magnetization. These materials are called
“soft ferromagnetic materials” (See adjacent
figure). Such materials are useful for
transformer, motor cores etc. where there is
continuous cycling of the magnetic field. A
fat loop (large coercive field) are called
“hard ferromagnetic materials”. Such
materials are useful for permanent magnets,
where there is no cycling of the magnetic field.
3) An addition to the ferromagnetic material used in the present experiment, there are
magnetic materials which are: a) Antiferromagnetic, b) Paramagnetic, c) Ferrimagnetic,
and d) Diamagnetic.
4) Antiferromagnetic: These have randomly oriented domains wherein two sets of atoms
have almost equal but anti-parallel moments. On applying a magnetic field, the domains
try to align with the magnetic field. The M-H curve is linear with a small slope.
5) Paramagnetic: Here each atom has magnetic moment, which are randomly oriented. On
application of external field, they try to align with the field, so long as the field is present.
On removal of the field, they are all again randomly oriented due to the thermal motion.
M-H curve is a straight line like for antiferromagnetic materials.
6) Ferrimagnetic: These atoms are organized in domains having two sets of atoms with
unequal moments, arranged in antiparallel sense. Each domain has overall aligned
moment. So they show M-H curve like ferromagnets, but with much less magnetization.
Iron oxide based insulating ceramic magnetic class of material called “ferrite” is most
commonly used ferrimagnetic material.
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BITS-Pilani K.K. Birla Goa Campus, Physics Department
PHY F214: Electromagnetics and Optics Laboratory
7) Diamagnetic: These atoms have no magnetic moment and as such they are not
magnetic materials. However, on application of external field, they generate induced
magnetic field in opposite sense, so as to repel the external field. They have M-H curve
like paramagnetic materials, but with negative slope.
8) Superconductors are most perfect diamagnetic materials. They do not allow any external
magnetic field to penetrate inside them, which leads to the “magnetic levitation” effect.
9) In the “Advanced Physics Lab” in the third year, you will have an experiment on
measurement of magnetic susceptibility of paramagnetic materials.
10) The table below summarizes the magnetic properties of all five types of materials
mentioned earlier, along with examples of each type. Variation of the reciprocal of the
susceptibility (χ) with temperature is also shown for each type of material. (Note: M = χ H).
Source:
ScienceDirect.com
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