Download magnetostatic (cont`d)

Biomedical Electronics Engineering, School of Mechatronics
ENT 215
Biomedical Electromagnetic Theory
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3.5 Faraday’s Law
In 1831, Michael Faraday had done an experiment
to prove that magnetic field could produce current.
He wound two separate windings on an iron toroid
and placed a galvanometer in one circuit and a
battery in the other. Upon closing the battery
circuit, there is deflection on galvanomater and
similar deflection in opposite direction when
battery diconnected.
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Faraday’s Law (cont’d)
A time-varying magnetic field produced an
electromotive force (emf) which then could produce
current in a closed circuit. An emf is merely a
voltage arises from conductors moving in a
magnetic field or from changing magnetic fields
emf  
d
dt
V
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Faraday’s Law (cont’d)
A non-zero value of dФ/dt may result from :
1) A time-changing flux linking a stationary closed
path.
2) Relative motion between a steady flux and a
closed path.
3) Combination of the two.
Minus sign tells that the emf is in such a direction
as to produce a current whose flux, if added to the
original flux would reduce the magnitude of the
emf. This is known as Lenz’s Law.
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Faraday’s Law (cont’d)
We can also define emf as :
emf   E  dL
This is a voltage about a specific closed path.
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Faraday’s Law (cont’d)
Given
Fm  qu  B
or,
Fm
 uB
q
Force per unit charge on the left hand of the
equation is called motional electric field intensity
Em,
Em  u  B
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Faraday’s Law (cont’d)
Finally we obtain,
emf   Em  dL   (v  B)  dL
This is the motional emf produced by moving
conductor.
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3.6 Magnetic Properties of Materials
Magnetic field can be enhanced by wrapping a
conductor wire around an iron core. The iron core
is considered as a magnetic material since it can
influence magnetic field. Different materials
actually have different degree of influence to
magnetic field.
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Magnetic Properties of Materials
(Cont’d)
We define magnetic susceptibility χm as the degree
of magnetization of material in response to an
applied magnetic field. While magnetization is the
property of materials that describes to what extent
they are affected by magnetic fields.
So, magnetization is
M  MH
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Magnetic Properties of Materials
(Cont’d)
Magnetization can also be defined as vector sum of
magnetic dipole moment per unit volume. In term
of magnetic flux density
B  0 H  0 M
We’ve also learned that B depends on relative
permeability of material, µr
B  0  r H
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Magnetic Properties of Materials
(Cont’d)
TYPES OF MAGNETIC MATERIALS
Diamagnetic - materials with µr slightly less than
one. Have very little influence on the magnetic
field. e.g bismuth
Paramagnetic - exhibit no magnetic behavior when
magnetic field absence. When magnetic field
present, magnetic dipole experiences a torque. e.g
aluminium
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Magnetic Properties of Materials
(Cont’d)
Ferromagnetic - strongly magnetic even in absence
of external applied field. Used for permanent
magnets e.g iron, nickel, cobalt
Superparamagnetic – ferromagnetic particles
suspended in a dielectric. Magnetization will
saturates at very large fields. e.g magnetic audio
and video tapes.
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3.7 Electromagnetic Flowmeter
The electromagnetic flowmeter measures
instantaneous pulsatile blood flow. It is based on
the principal that electric magnetic force will be
induced if a conductor is cutting through a
magnetic field.

e   v  BdL
l
0
Where
 B: Magnetic flux density, in the unit of T
 L: length of conductor, in the unit of m
 U: instant velocity of the blood, in the unit of m/s
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Electromagnetic Flowmeter (cont’d)
When the directions of the velocity, magnetic flux
density and the conductor are perpendicular to
each other, the electric magnetic force is easily
determined as indicated in the following equation.
e = BLv
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Electromagnetic Flowmeter (cont’d)
PROBE DESIGN
The toroidal-type cuff probe has two
oppositely wound windings on each
half of the core. The magnetic flux
thus leaves the top of both sides,
flows down in the center of the cuff,
enters the base of the toroid and flows
up through both sides. The electrodes
are mounted at the center of the both
sides of the toriod. This probe can be
easily fit snuggly to the vessel. Choose
proper size of the probe based on the
size of the blood vessel.
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Electromagnetic Flowmeter (cont’d)
Unfortunately there is error in measurement
caused by :
1)
2)
3)
4)
Velocity profile is asymmetric especially around the curve of aorta.
Shunting effects of the wall of blood vessel.
Circulating currents flow in the axial direction.
Magnetic flux density is not uniform in the transverse plane.
Callibration is recommended before measuring to
overcome these errors.
EM flowmeter actually can be used to measure the
flow of all types of counducting liquid.
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PRACTICAL APPLICATION
Transformer
A current passing through the primary coil
creates a magnetic field. Changing
magnetic field within a coil of wire induces
a voltage across the ends of the coil. By
changing the current in the primary coil, it
changes the strength of its magnetic field;
since the changing magnetic field extends
into the secondary coil, a voltage is
induced across the secondary. The primary
and secondary coils are wrapped around a
core of very high magnetic permeability,
such as iron
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LOUDSPEAKERS
• Paper or plastic cone
affixed to a voice coil
(electromagnet) suspended
in a magnetic field.
136)
•AC Signals to the voice
coil  moves back and
forth, resulting vibration of
the cone and producing
sound waves of the same
frequency as the AC signal
ving-coil loudspeaker.
Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth
Copyright © 2005 by John Wiley & Sons. All rights reserved.
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MAGLEV
igure 3-53 (p. 159)
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MAGLEV (Cont’d)
amentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth
Copyright © 2005 by John Wiley & Sons. All rights reserved.
• Interaction between
electromagnets in the train and
the current carrying coils in the
guide rail provide levitation.
• By sending waves along the
guide rail coils, the train magnet
pushed/pulled in the direction of
travel. The train is guided by
magnet on the side of guide rail.
• Computer algorithms maintain
the separation distance.
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