Lec 4

1. 1
Applications of Electrical Stimulation
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Vision restoration
Epilepsy control
Tremor control
Phrenic pacing
Control of reaching
and grasping
Scoliosis control
Muscles exercise
Control of standing
and walking
Spasticity reduction
Cochlear implant
Cardiac pacing
Bowel emptying
Bladder empting and
control of incontinence
Wound healing
Pain suppression
2
Magnetostatic Fields
• The other half of electromagnetics is the magnetic field.
• Whereas electric fields emanate directly from individual charges,
magnetic fields arise in a subtle manner because there are no
magnetic charges.
• Moreover, because there are no magnetic charges, magnetic field
lines can never have a beginning or an end (Magnetic field lines
always form closed loops).
• Some physicists have been searching for magnetic charges (or
“magnetic monopoles,” as the particle physicists call them) in high
energy experiments.
• Without magnetic charges, magnetic fields can only arise indirectly.

2. 2
3
• Magnetic fields are generated indirectly by moving electric
charges.
• It is a fundamental fact of nature that moving electrons, as well
as any other charges, produce a magnetic field when in motion.
• Electrical currents in wires also produce magnetic fields because
a current is basically the collective movement of a large number
of electrons.
• A steady (DC) current through a wire produces a magnetic field
that encircles the wire.
right hand rule
B I
4
• Magnetic Dipole
• If a current travels in a loop, the magnetic field is donut-shaped.
• The magnetic field flows out of one side and back in the other side.
• Although the field lines still form closed loops, they now have a
sense of direction. The side where the field lines emanate is called
the north pole, and the side they enter is called the south pole.
• Such a structure is called a magnetic dipole.
• Now if a wire is wound in many spiraling loops, a solenoid is
formed. A solenoid concentrates the field into even more of a dipole
structure.
NS

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5
• A magnetostatic field is produced by a constant current flow (or
direct current).
• This current flow may be due to magnetization currents as in
permanent magnets, electron-beam currents as in vacuum tubes,
or conduction currents as in current-carrying wires.
• There are two major laws governing magnetostatic fields:
•
(1) Biot-Savart's law, and
(2) Ampere's circuit law.
Similar to Coulomb's law, and Gauss's law in electrostatics
6
The Biot-Savart's Law
• The Biot-Savart's law states that the magnetic field intensity dB produced at a point
X by the differential current element dl is proportional to the product dl and the sine
of the angle between the element and the line joining X to the element and is
inversely proportional to the square of the distance r between X and the element.
0
2
4
dl a
dB rI
r




r
Idl
dBâr x
d = b  c = |b||c|sin(F) â

4. 4
7
The Biot-Savart Law
r
I
dl
dB
âr
x
0
2
4
dl a
dB rI
r




8
r
âr
Example of Biot-Savart Law : Infinite Line
of Current
dl
0 0
2 2
,
4 4
dl a dl a
dB B
l
r r
l
I I
r r
 
 






 
 

.
dB
If

5. 5
9
dB
âr
I
dl
.
f
dl
f
df
df
r
0
2
4
dl a
dB rI
r




 sinR r f
f
ff
f
sin
,sin
rd
dl
dl
rd

10
âr
dl
F
0
2
4
dl a
dB rI
r




 1 sin f   dl a , out of the diagramr dl
   
 
 0
0 00
2 2
sin
sin
4 44
s
4
in ns i
 f
 f  f f
 
f

f

f
 
 
     dB
r
I
Idl I dI
r
d
d
dB
r r R
f
f
sin
rd

6. 6
11
 0 sin
4
I d
dB
R
 f f


 
 
180
0 0
0
sin
sin
4 4
I d I
B dB d
R R
f
f
 f f 
f f
 
 
  
   
   
1800 0 0
0
cos 1 1
4 4 2
I I I
B
R R R
f
f
  
f
  
 
 
      
   
1800 0 0
0
cos 1 1
4 4 2
I I I
B
R R R
f
f
  
f
  
 
 
      
0
2


Β a, where a points out of the page
I
R
12
Gauss’s Law for the Magnetic Field-Integral
Form

7. 7
13
Gauss’s Law-Differential Form
   BdvdaB
Divergence Theorem:
The flux of a vector through a closed
surface is equal to the integral of the
divergence of the vector taken over the
volume enclosed by that closed surface
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Biot-Savart Law
• Like Coulomb’s Law – always works in principle
– The example we have just looked at is “high-symmetry”
– i.e. an infinite, infinitesimally-narrow “rod” of current
• If there’s not much symmetry, the integrals can be
difficult/impossible
• Is there a magnetic-field equivalent of Gauss’ Law?
• Yes – thanks to Professor Ampere

8. 8
15
Ampere’s Law –Integral Form
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Ampere’s Law –Differential Form

9. 9
17
B?
Example
• Calculate the magnetic field H both
Outside (>a)
and
Inside (<a)
A wire with uniformly-distributed current I,
current density
I
B? |J| = I/A
a
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Outside … >a, H.dl = Ienclosed
enclosed
c
IadHdlH  F 2
ff
I
a
B
H, B
fff

a
I
aHH
2


10. 10
19
B?
Inside … <a, H.dl = Ienclosed
I, |J|=I/a2
a
I
   
fff
f

f





f
a
a
I
aHH
a
I
H
IadHa
inside 2
2
2
2
0
2
2



20
2
I
H 
B,H

2
2 a
I
H




11. 11
21
22
Magnetization in materials
• Assuming that our atomic model is that of an electron orbiting about a positive
nucleus.
• A given material is composed of atoms. Each atom may be regarded as
consisting of electrons orbiting about a central positive nucleus; the electrons also
rotate (or spin) about their own axes.
• Thus an internal magnetic field is produced by electrons orbiting around the
• nucleus (a) or electrons spinning (b).
• Both of these electronic motions produce internal magnetic fields B, that are
similar to the magnetic field produced by a current loop.

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Permeability &Susceptibility
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Classification of Magnetic Materials
• In general, we may use the magnetic susceptibility m or the
relative permeability µr to classify materials in terms of their
magnetic property or behavior.
• A material is said to be nonmagnetic if m = 0 (or µr = 1); it is
magnetic otherwise.
• Roughly speaking, magnetic materials may be grouped into three
major classes: diamagnetic, paramagnetic, and ferromagnetic.

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Diamagnetism (Self study)
• Diamagnetism occurs in materials where the magnetic fields due to electronic
motions of orbiting and spinning completely cancel each other.
• Thus, the permanent (or intrinsic) magnetic moment of each atom is zero and
the materials are weakly affected by a magnetic field.
• For most diamagnetic materials (e.g., bismuth, lead, copper, silicon, diamond,
sodium icon, chloride), m is of the order of 10 -5.
• In certain types of materials called superconductors at temperatures near
absolute zero, "perfect diamagnetism" occurs: m = -1 or 1 or µr = 0 and B = 0.
Thus superconductors cannot contain magnetic fields.
• Except for superconductors, diamagnetic materials are seldom used in
practice.
• Diamagnetism is an extremely weak effect. Even though all materials exhibit
diamagnetism, the effect is so weak that you can usually ignore it.
• This explains the commonly known fact that most materials are not affected by
magnets.
• Materials whose atoms have nonzero permanent magnetic moment may be
paramagnetic be paramagnetic or ferromagnetic.
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Paramagnetism (Self study)
• Paramagnetism occurs in materials where the magnetic fields produced by orbital and
• spinning electrons do not cancel completely.
• Unlike diamagnetism, paramagnetism is temperature dependent..
• For most paramagnetic materials (e.g., air, platinum, tungsten, potassium), m is of the
• order +10-5 to +10 -3 and is temperature dependent.
• Paramagnetism, while stronger than diamagnetism, is another very weak effect and can
usually be ignored.
• The reason for its weakness is that the electrons in each atom are always grouped in
pairs that spin opposite to one another.
• Hence, paramagnetism can only occur in atoms that have an odd number of electrons.
• For example, aluminum has an atomic number of 13 and thus has an odd number of
electrons. It therefore exhibits paramagnetic properties.
• The random thermal motions of the atoms tend to prevent the dipole moments from
lining up well, even when exposed to an external field.
• Such materials find application in masers (a device or object that emits coherent
microwave radiation produced by the natural oscillations of atom or molecules between
energy levels).

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Ferromagnetism
• A ferromagnetic material is like a paramagnetic material with the added
feature of “domains.”
• Each domain is a microscopic patch of billions of atoms that have all
lined up their dipole moments in the same direction.
• It so happens that the quantum mechanical properties of certain
materials, notably iron, cause these domains to form spontaneously.
This is due to the electron spin and to the collective behavior of the
outermost electrons of large groups of atoms.
• Normally, the domains are randomly oriented so that the material still
has no overall magnetic dipole.
• However, when a magnetic field is applied the domains that align to
the field grow, while domains of other orientations shrink.
• In addition, the domains have a tendency to freeze in place after
aligning. In other words, ferromagnetic materials have memory. For
example, if a bar of iron is placed in a strong field and then removed,
the bar retains a net magnetic dipole moment. It has become a magnet.
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• Some other examples of ferromagnetic materials are nickel and cobalt.
• Several metal alloys are also ferromagnetic.
• Ferromagnetic materials have the following properties: They lose their
ferromagnetic properties and become linear paramagnetic materials
when the temperature is raised above a certain temperature known as
the curie temperature.
• Thus if a permanent magnet is heated above its curie temperature
(770°C for iron), it loses its magnetization completely.
• They are nonlinear; that is, the constitutive relation the B = µoµrH does
not hold for ferromagnetic materials because µr depends on B and
cannot be represented by a single value.

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•Permeability quantifies how a material responds to magnetic fields in a manner
analogous to how permittivity quantifies the material response to an electric field.
•Permeability is a measure of the magnetic energy storage capabilities of a material. A
material with a relative permeability of 1 is magnetically identical to a vacuum, and
therefore stores no magnetic energy.
Paramagnetic and ferromagnetic materials have relative permeability greater than 1,
which implies that the material aligns its dipole moments to an induced field and
therefore stores energy.
•Higher permeability translates to a larger reaction and higher energy storage.
• Diamagnetic materials are characterized by relative permeabilities less than 1.This
fact implies that the material aligns its dipole moments opposite to an induced field.
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16. 16
Assignment
1. What possible health effects of static magnetic
fields have been studied in the literature? (List at
least five).
2. Explain the theory and the uses of the following:
Iontophoresis, Neuromuscular stimulation,
Transcutaneous nerve stimulation
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