Electro-magnetic flow meters
Information from Alltron Instruments
Hans Christian Oersted discovered that an electric current can produce a magnetic field - the more current you have the more flux you
generate.
That is easy enough to grasp. What needs a firm
intellectual grip is to appreciate that Faraday’s
Law does not stop operating just because you
have current flowing in the coil. When the coil
current varies then that will alter the flux and,
says Faraday, if the flux changes then you get an
induced voltage. This merry-go-round between
current, flux and voltage lies at the heart of
electromagnetism. Calculating the sequence of
operation just described is quite easy.
In electric motors and generators you will
usually have more than one of these causes at
the same time. It doesn’t matter what causes
the change; the result is an induced voltage,
and the faster the flux changes the greater the
voltage.
The transformer equation that the induced
voltage will oppose the externally applied
voltage which made the current change (Lenz’s
law). This creates a limit to the rate of rise of the
current and prevents (at least temporarily) the
melt-down we get without coiling.
Take an example of an inductor having 7 turns
and in which the flux varies according to
The effect of coil current
The ‘flip side to Faraday’
Equation FYS
Now let’s spin our fairground ride in the other
direction. Instead of getting an induced voltage
by putting in a current we’ll put a voltage across
the coil and see what happens. Normally, if you
put several volts across any randomly arranged
bit of wire then what will happen will be a
flash and a bang; the current will follow Ohm’s
law and (unless the wire is very long and thin)
there won’t be enough resistance to prevent
fireworks. It’s a different story when the wire
is wound into a coil. If the current increases
then we get flux build up which induces a
voltage of its own. The sign of this induced
voltage is always such that the voltage will be
positive if the current into the coil increases.
We say Michael Faraday’s greatest contribution
to physics was to show that a voltage, e, is
generated by a coil of wire when the magnetic
flux, Φ enclosed by it changes
Substituting this into Faraday’s law
Calculating this ‘flip side to Faraday’ is also
easy; we take his law in its differential form
above and integrate:
The integral form of Faraday’s law where e
is the externally applied voltage and N is the
number of turns.
Inductor with AC applied
So our winding will have a peak voltage of
16,8 V. We can easily generalise this for any flux
varying sinusoidally at a frequency f to show
(The transformer equation)
Let’s apply a sinusoidal voltage, frequency f,
RMS amplitude a:
Substituting this into the integral form of
Faraday:
Faraday’s Law
A nearby permanent magnet is moving about.
•
The coil rotates with respect to the magnetic
field.
•
The coil is wound on a core whose effective
permeabilty changes.
•
The coil is the secondary winding on a
transformer where the primary current is
changing.
Elektron June 2005
Fig. 1: Current build-up in a 820 mH inductor.
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The expression with the limits of integration will
always be between -1 and +1 so that the peak
value of flux is given by
Compare this with the transformer equation
above.
Example: If 230 V at 50 Hz is applied to an
inductor having 200 turns then what is the peak
value of magnetic flux?
One important general point: if your winding
has to cope with a given signal amplitude then
the core flux is proportional to the inverse of
the frequency. This means, for example, that
mains transformers operating at 50 or 60 Hz are
larger than transformers in switching supplies
(capable of handling the same power) working
at 50 kHz.
Using inductance
If the material permeability is constant then the
relation between flux and current is linear and,
by the definition of inductance :
where L is the inductance of the coil. Substituting
into the integral form of the law:
If e is a constant then this formula for the current
simplifies to:
Example: If a 820 mH coil has 2 volts applied
then find the current at the end of three
seconds.
Conclusion: why Faraday is cool
Satisfy yourself that this result above is consistent
with our original formulation of Faraday’s law:
voltage is proportional to the rate of change of
flux. Consider also how useful this integration
method is in practical inductor design; if you
know the number of turns on a winding and
the voltage waveform on it then you integrate
with regard to time and voilá you have found
the amount of flux. What’s more is that you
found it without knowing about the inductance
or the core: its permeabilty, size, shape, or even
whether there was a core at all.
Postscript: Time to wave goodbye
It was deduced in 1862 by James Clerk Maxwell
that the converse happens: that a changing
E-field produces a magnetic field. Put the two
together, that a change in one gives the other
and vice-versa, and you might wonder where
it all ends. In fact it ends with a dance between
the two forms of energy in which E and M
continually rub shoulders within what is called
an electromagnetic wave - of which light, radio
and X-rays are all examples. Maxwell expresses
Faraday’s law in a more general vector field
equation -
Maxwell’s equation for E
Contact Rudi Tuffek, Alltron Instruments,
Tel (011) 314-6229, rudi@alltron.co.za ‰
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Elektron June 2005