**Theory of Magnetic Cores & Magnetism
Tutorial**

** I****f the bible were
rewritten, the book of ***Genesis* should start with: "In the
beginning HE created the electron. " Lets’ call it here the e- !

**The e- is the most important thing in all of electrical
engineering, despite the fact, that nobody knows what it really is. According to
physicists it can be a particle as well as a Wave. Strange? How can anything be a particle and a wave at
the same time ??? WRONG !!! NOT at the same time! If you show it being a
particle, it forgets being a wave, if you show the wave character it does not
show itself as a particle ! Einstein considers these things higher-dimensional (length,width,height,time
and whatelse ??} If you project such a thingie into our 3 or 4 dimensional
world, it will have multiple 3D or 4D projections which do not necessarily make sense to
our thinking.**

**In an atom the e- is said to orbit around the nucleus.
(seemingly as a particle) but it is the wavefunction that tells the probability
where it is at a certain moment. ONLY the probability, because Heisenberg says
that location and speed can only be determined together with a certain minimum
error, In other words: If you know where it is, you cannot tell where it’s
going, and if you know it’s speed, you cannot tell where it is………**

**e- has an electric charge, so it can be accelerated by a
voltage (not only in a wire, but also in a vacuum (see CRT). It also has
something physicists stupidly call "spin" which has nothing to do with
it spinning around it’s axis.(What axis ????} That spin comes ONLY** ** in 2 kinds, up and down. (referred to what ???) and has
something to do with Magnetism, for which there is only a sketchy description as a condition
of space that makes a compassneedle move. Also, you can NOT distinguish one e- from another, they are
all the same and you can NOT label one e- such that it stands out from the others. No
Way !!!**

**If an e- moves, its charge moves and if a charge moves, that
is called a current. No sense, asking, why the charge moves, it doesn’t
matter! It takes 1.6E16 e- (yes, that’s 16 Zeroes after the One) every second
to move past a certain point to make 1 Ampère !!! That’s a bunch !!! If that
Amp flows for one second into a 1 Farad Capacitor (A big one !) it raises
The Voltage on the capacitor by one Volt. An Amp flowing a sec
long is called a Coulomb.[Cb](That’s charge). And 1 Cb into 1 F makes 1V. (1
Cb into 1 µF would make 1 MV, keep fingers off !**

**If a current flows, all the tiny magnets of the e-‘s line up
to add together to a much bigger Magnetic field which does NOT move, but stands still as long
as the current keeps flowing unchanged. If the current flows in a wire, that
field wraps itself around the wire and gets weaker, the farther away from the wire you go to
measure it. And if you flow the current through a turn of wire and stick a
magnetic material into the center, this core will concentrate the fields along
its length which is perpendicular to the plane of the turn. (Magnetic field is
always @ 90º to the direction of the current) . Unfortunately, the core does
not catch ALL of the field, some squeezes through between the turn and the core
and that part is called leakage flux. (There is no such thing as an insulator
for magnetism).**

**You run that wire around twice, you have 2 turns. But, since
you cannot label individual e-‘s , you cannot label individual currents, so,
the field sees 2 currents of the same strength and gets twice as strong, even if
the 2 currents come from different sources! So, the important quantity is NOT Amps or Turns, it is
Ampereturns (AT}and the field sums up all the contributing AT’s. And the core
concentrates this field and kind of multiplies it by the permeability [µ] of
the core material and the result is the active field in the device. This goes on
until the AT’s are so high that the material reaches saturation and says:
Yechch, I can no more!!! Then the leakage increases because the excess field now
bypasses the core and any further increase of AT’s is useless for most
practical purposes. The magnetization in the core is the Gausses [G] and it gets
higher as the AT’s increase and lower as the cross-section of the core increases
and as the magnetic pathlength of the core increases. So another important
parameter for the Gausses is the AT’s per square inch of core! But, the length
of the magnetic path in the core comes into play too, so first you have Amperes
per meter which times a weird factor become Oersteds.(Oe). And the Oersteds
multiplied by the effective permeability of the core become the Gausses.
Naturally in their infinite wisdom, the standards people could not leave well
enough enough, so they screwed up systems and we have Webers and Teslas and
other new (old) names around, but just let’s be happy with Oe & G . (The
old mho is now a Siemens but who uses that ???).**

**The magnetic material is such characterizes by the
magnetization curve, where the x-axis is calibrated in Oe and the y-axis in G.
So, if you have a completely demagnetized material, this curve starts at the
Origin (0/0), rises linearly and then bends over and reaches a saturation value.
This is the virgin curve.[Never thought there would be electrical or magnetic
virgins….] . Now when you reduce the Oe to 0, the curve will NOT retrace but
will cross the y Axes at a point above 0, so with 0 Oe there will still be some
G left and that is the Remanence. The core stays slightly magnetic ! If you do
that with a Cobalt steel or with Alnico or other selected materials, a lot of G’s
will be left at the 0 Oe point and you have now a permanent magnet !! By the way, the tangent of the angle at which the virgin
leaves the origin (if you plot it as a straight line) (G/Oe) is the initial
permeability µsub0 and that’s what the manufacturer advertises since is
higher than the µ anywhere else (despite the fact that in actual use it does
not mean a thing)**

**Now, if you start applying negative Oe’s (by reversing the
current) the G’s will go down from the remanence point and will reach 0. The
Oe needed to do that are called the coercive force. Go farther with you negative
Oe’s and you will now trace a G/Oe curve in the third quadrant into saturation
and back to a negative remanence value. Now your Oe’s must go positive again
and you trace a G/Oe curve in the first quadrant and so on---and so on…. At
any point of these curves , the steepness (which is the angle of the tangent to
the curve at this point [dG/dOe] is the effective permeability at that point.
But you will never get back to the virgin !!! But when you go into saturation,
the curve has bent to almost parallel to the Oe axis so the G’s don’t
increase much when the Oe’s increase so the perm tends to go to 0. (Really to
1, because that’s the perm of empty space, so, effectively, the core has
disappeared, or you are now left with an air core which has a perm of very close
to 1.) But, efficient cores have perms in the 1000’s or 10’000’s so the
saturation point perm of 1 is so negligible, you may as well call it 0 and state
that at saturation the perm disappears !**

*Hans R. Meyer P.E.*