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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

Vdt

demf

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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 :

This is a voltage about a specific closed path.

LE demf

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Faraday’s Law (cont’d)

Given

or,

Force per unit charge on the left hand of the equation is called motional electric field intensity Em,

BuF qm

BuF

qm

BuE m

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Faraday’s Law (cont’d)

Finally we obtain,

This is the motional emf produced by moving conductor.

LB(vLEm dd )emf

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3.6 Magnetic Properties of Materials

Magnetic field can be enhanced by wrapping aconductor 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 HM M

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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

We’ve also learned that B depends on relative permeability of material, µr

MHB 00

0 HB r

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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.

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

l

LdBve0

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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

SN

FLOW

AppliedMagneticField

Inducede.m.f.

To detector circuit

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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) Velocity profile is asymmetric especially around the curve of aorta.

2) Shunting effects of the wall of blood vessel.

3) Circulating currents flow in the axial direction.

4) 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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• Paper or plastic cone affixed to a voice coil (electromagnet) suspended in a magnetic field.

•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

LOUDSPEAKERS

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MAGLEV

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MAGLEV (Cont’d)

• 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.