The document discusses various magnetic properties of materials including diamagnetism, paramagnetism, and ferromagnetism. It also covers topics like magnetization, hysteresis, inductance, relative permeability, eddy currents, ferrites, transformers, and magnetic circuits. As an example, it calculates the inductance of a solenoid coil with given parameters and of a toroidal coil.

6. Applied Magnetism
Wang C. Ng
Sep. 21, 2009
wang.ng@scc.losrios.edu
(916)558-2638

7. References:
• http://hyperphysics.phy-astr.gsu.edu/hbase
; 9-13-2009.
• http://www.magnet.fsu.edu/; 9-13-
2009.
• http://www.hobbyprojects.com/componen
; 9-13-2009.
• http://www.electronicsteacher.com/electr
; 9-14-2009.
• J.J.Cathey & S.A.Nasar; Basic

8. Magnetic Properties of
Solids
• Materials may be classified by
their response to externally
applied magnetic fields as
diamagnetic, paramagnetic, or
ferromagnetic.
• These magnetic responses
differ greatly in strength.
• Diamagnetism is a property of
all materials and opposes

9. Magnetic Properties of
Solids
• Paramagnetism is stronger than
diamagnetism and produces
magnetization in the direction of
the applied field, and proportional
to the applied field.
• Ferromagnetic effects are very
large, producing magnetizations
sometimes orders of magnitude
greater than the applied field and
as such are much larger than

10. Magnetization
• The magnetization of a material is
expressed in terms of density of
net magnetic dipole moments m in
the material.
• We define a vector quantity called
the magnetization M =
μtotal/Volume.
• The total magnetic field B in the
material is given by B = B0 +
μ0M

11. • Another way to view the magnetic
fields which arise from
magnetization of materials is to
introduce a quantity called
magnetic field strength H .
• It can be defined by the relationship
H = B0/μ0 = B/μ0 – M
• H has the value of unambiguously
designating the driving magnetic
influence from external currents in
a material, independent of the
Magnetization

12. • H and M have the same units,
amperes/meter.
• The relationship for B and H
above can be written in the
equivalent form
B = μ0 (H + M) = μr μ0 H, where μr
= (1 + M/H)
• The relative permeability µr can be
viewed as the amplification factor
for the internal field B due to an
Magnetization

13. Diamagnetism
• The orbital motion of electrons
creates tiny atomic current loops,
which produce magnetic fields.
• When an external magnetic field is
applied to a material, these current
loops will tend to align in such a
way as to oppose the applied field.
• This may be viewed as an atomic
version of Lenz's law: induced
magnetic fields tend to oppose the
change which created them.

14. Diamagnetism
• All materials are inherently
diamagnetic, but if the atoms
have some net magnetic moment
as in paramagnetic materials or in
ferromagnetic materials, these
stronger effects are always
dominant.
• Diamagnetism is the residual
magnetic behavior when
materials are neither

15. Diamagnetism
• Any conductor will show a strong
diamagnetic effect in the
presence of changing magnetic
fields because circulating
currents will be generated in the
conductor to oppose the magnetic
field changes.
• A superconductor will be a
perfect diamagnet since there is
no resistance to the forming of
the current loops.

16. Paramagnetism
• Some materials exhibit a
magnetization which is
proportional to the applied
magnetic field in which the
material is placed.
• These materials are said to be
paramagnetic and follow Curie's
law:

17. Paramagnetism
• All atoms have inherent sources
of magnetism because
electron spin contributes a
magnetic moment and electron
orbits act as current loops which
produce a magnetic field.
• In most materials the magnetic
moments of the electrons cancel,
but in materials which are
classified as paramagnetic, the

18. Ferromagnetism
• Iron, nickel, cobalt and some of
the rare earths (gadolinium,
dysprosium) exhibit a unique
magnetic behavior which is called
ferromagnetism because iron
(ferrum in Latin) is the most
common and most dramatic
example.
• Samarium and neodymium in
alloys with cobalt have been used
to fabricate very strong
rare-earth magnets.

19. Ferromagnetism
• Ferromagnetic materials exhibit a
long-range ordering phenomenon
at the atomic level which causes
the unpaired electron spins to line
up parallel with each other in a
region called a domain.
• Within the domain, the magnetic
field is intense, but in a bulk
sample the material will usually
be unmagnetized because the
many domains will themselves be

20. Ferromagnetism
• Ferromagnetism manifests itself
in the fact that a small externally
imposed magnetic field, say from
a solenoid, can cause the
magnetic domains to line up with
each other and the material is
said to be magnetized.
• The driving magnetic field will
then be increased by a large
factor which is usually expressed
as a relative permeability for the

21. Ferromagnetism
• There are many applications of
ferromagnetic materials, such as the
electromagnet.
• Ferromagnets will tend to stay
magnetized to some extent after
being subjected to an external
magnetic field.
• This tendency to "remember their
magnetic history" is called
hysteresis.
• The fraction of the saturation

22. Ferromagnetism
Hysteresis

23. Ferromagnetism
• All ferromagnets have a maximum
temperature where the
ferromagnetic property disappears
as a result of thermal agitation.
• This temperature is called the
Curie temperature.
• Ferromagntic materials respond
mechanically to an impressed
magnetic field, changing length
slightly in the direction of the
applied field.

24. Ferromagnetic
MaterialsMaterial Treatment
Initial Relative
Permeability
Maximum Relative
Permeability
Coercive
Force
(oersteds)
Remanent Flux
Density
(gauss)
Iron, 99.8% pure Annealed 150 5000 1.0 13,000
Iron, 99.95% pure Annealed in hydrogen 10,000 200,000 0.05 13,000
78 Permalloy Annealed, quenched 8,000 100,000 .05 7,000
Superpermalloy
Annealed in hydrogen,
controlled cooling
100,000 1,000,000 0.002 7,000
Cobalt, 99% pure Annealed 70 250 10 5,000
Nickel, 99% pure Annealed 110 600 0.7 4,000
Steel, 0.9% C Quenched 50 100 70 10,300
Steel, 30% Co Quenched ... ... 240 9,500
Alnico 5
Cooled in magnetic
field
4 ... 575 12,500
Silmanal Baked ... ... 6,000 550
Iron, fine powder Pressed ... ... 470 6,000

25. Inductance (review)

26. Inductance (review)
• Increasing current in a coil of wire
will generate a counter emf which
opposes the current.
• Applying the voltage law allows us
to see the effect of this emf on the
circuit equation.
• The fact that the emf always
opposes the change in current is
an example of Lenz's law.
• The relation of this counter emf to
the current is the origin of the

27. Inductance (review)
• Inductance of a coil: For a fixed
area and changing current,
Faraday's law becomes
• Since the magnetic field of a
solenoid is
then for a long coil the emf is
approximated by

28. Inductance (review)
• From the definition of inductance
we obtain

29. Relative Permeability
• The magnetic constant μ0 = 4π x
10-7
T m/A is called the
permeability of space.
• The permeabilities of most
materials are very close to μ0
since most materials will be
classified as either paramagnetic
or diamagnetic.

30. Relative Permeability
• But in ferromagnetic materials the
permeability may be very large
• It is convenient to characterize
the materials by a relative
permeability.

31. Relative Permeability
• When ferromagnetic materials are
used in applications like an
iron-core solenoid, the relative
permeability gives you an idea of
the kind of multiplication of the
applied magnetic field that can be
achieved by having the
ferromagnetic core present.
• For an ordinary iron core you
might expect a magnification of
about 200 compared to the

32. Relative Permeability
• This statement has exceptions
and limits, since you do reach a
saturation magnetization of the
iron core quickly, as illustrated in
the discussion of hysteresis.

33. Eddy Currents
• Currents that are induced into a
conducting core due to the
changing magnetic field.
• Eddy currents produce heat which
results a loss of power
• This effect can reduce the
efficiency of an inductor or a
transformer.
• The Eddy current loss is
proportional to f 2
.
http://www.magnet.fsu.edu/education/t

34. Ferrites
• Compound composed of iron
oxide, metallic oxide, and
ceramic.
• The metal oxides include zinc,
nickel, cobalt or iron.
• A powdered, compressed and
sintered magnetic material having
high resistivity.
• The high resistance makes eddy
current losses low at high
frequencies.

35. Ferrites vs. iron cores
• Iron cores are used for
frequencies below about 100 kHz.
• Ferrite cores are used for
frequencies up to say, 10 MHz.
• Above 100MHz the core is usually
air and the coil is self supporting.

36. Ferrites vs. iron cores
• At low frequencies the inductor
may have hundreds of turns,
above 1 MHz only a few turns.
• Most inductors have a low DC
resistance since they are wound
from copper wire.

37. Inductance of a
Solenoidhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/ind

38. Inductance of a
Solenoid
Solenoid length = 10 cm with N =
200 turns,
Coil radius r = 1 cm gives area A =
3.14159 cm2
.
Relative permeability of the core k
= 200,
Then the inductance of the solenoid
is
L = 31.58 mH.

39. Inductance of a
Solenoid
• Small inductors for electronics
use may be made with air cores.
• For larger values of inductance
and for transformers, iron is used
as a core material.
• The relative permeability of
magnetic iron is around 200.
• This calculation makes use of the
long solenoid approximation.

40. Approximate Inductance
of a Toroid
• Finding the magnetic field inside a
toroid is a good example of the
power of Ampere's law.
• The current enclosed by the
dashed line is just the number of
loops times the current in each
loop.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indtor.html#c1

41. Approximate Inductance
of a Toroid
• Amperes law then gives the
magnetic field at the centerline of
the toroid as

42. Approximate Inductance
of a Toroid
• The inductance can be calculated
in a manner similar to that for any
coil of wire.

43. Approximate Inductance
of a Toroid
Toroidal radius r = 5 cm with N = 200
turns,
Coil radius = 1 cm gives area A =
3.14159 cm2
.
Relative permeability of the core k =
200,
Then the inductance of the toroid is
approximately
L = 10.053 mH.

44. Approximate Inductance
of a Toroid
• Small inductors for electronics
use may be made with air cores.
• For larger values of inductance
and for transformers, iron is used
as a core material.
• The relative permeability of
magnetic iron is around 200.

45. Approximate Inductance of
a Toroid
• This calculation is approximate
because the magnetic field
changes with the radius from the
centerline of the toroid.
• Using the centerline value for
magnetic field as an average
introduces an error which is small
if the toroid radius is much larger
than the coil radius.

46. Transformer
• A transformer makes use of
Faraday's law and the
ferromagnetic properties of an
iron core to efficiently raise or
lower AC voltages.
• A transformer cannot increase
power so that if the voltage is
raised, the current is
proportionally lowered and vice
versa.

47. Transformer

48. Magnetic Circuits
• A magnetic circuit is a path for
magnetic flux, just as an electric
circuit provides a path for the
flow of electric current.
• Transformers, electric machines,
and numerous other
electromechanical devices utilize
magnetic circuits.
• If the magnetic field B is uniform
over a surface A and is
everywhere perpendicular to the
/www.magnet.fsu.edu/education/tutorials/java/magneticshunt/index

49. Magnetic Circuits
• The effectiveness of electric
current in producing magnetic
flux is defined as the
magnetomotive force = N I.
• The reluctance of a magnetic
circuit is defined as: = / φ
• Ohm’s law: R = V / I
R = l / σ A
= = l / μ A

50. Magnetic Circuits
• Differences between a resistive
circuit and a magnetic circuit:
• There is I 2
R loss in a resistive circuit
but no φ 2
loss in a reluctance.
• Magnetic flux can leak to the
surrounding space.
• A magnetic circuit can have air gaps.
• In general, the permeability μ is not
a constant.

51. Magnetic Circuits
• Mutual inductance:
• (coupling coefficient) is
defined as the fraction of the flux
produced by the qth
coil that links
the pth
coil.
• ≅ 1 if fringing is negligible.

52. Magnetic Circuits
• Finally, the self and mutual
inductances can be computed
from the following formula:

53. Magnetic Circuits
Example: The core of a magnetic circuit is of
mean length 40 cm and uniform cross-sectional
area 4 cm2
. The relative permeability of the
core material is 1000. An air gap of 1 mm is cut
in the core, and 1000 turns are wound on the
core. Determine the inductance of the coil if
fringing is negligible.

54. Thank YOU