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From: firstname.lastname@example.org (Roy McCammon)
Subject: Re: Deriving H for magnetic cores
Date: Tue, 17 Dec 2002 14:57:10 -0600
X-Mailer: Mozilla 4.5 [en]C-CCK-MCD 3M/NCP 4.5 (WinNT; I)
"Christopher R. Carlen" wrote:
> I have just about had it with inconsistent H and B formulas
they say each formula halves the number of people who will
read your post all the way through.
> First off, let's at least agree on
> Ampere's Law for magnetostatics:
> H_vec . dl_vec = I
> H_vec = phi_hat*H
only in certain special cases, the perfect toroid happens
to be the only one that I know of. This is important
this is the easy one that the books have, but which is
> Now we can squabble about the assumptions that must be made in order to
> use Ampere's Law. The most important assumption is that H=|H_vec| is
> uniform over any C. Any counters to this assumption?
That is pretty much the important assumption.
Generally requires axial symmetry and that
the phi_hat component of current be zero.
> We expect to see variation in H vs. r ; that will be accounted for in
> this treatment.
or z, but not phi.
> The other assumption regards the accounting for the magnetic flux
> developed by H as being located almost entirely inside the core.
Not necessary if you have the proper axial symmetry, you
know that the phi_hat component of H is the only non-zero
component and | H | is independent of phi. From this you
can conclude that any circle that is parallel to the toroid
and centered on its axis is a contour of constant H (in
the phi_hat coordinate). Any such contour that
is not enclosed inside the toroid will encircle zero
current hence the line integral of H is zero and since
it is a contour of constant H (in the phi_hat direction),
it must be a contour where H = 0.
> is a subject about which I am still confused. I grew accustomed to
> calculating fields in uniform regions of permeability, using the
> Biot-Savart Law before learning to use Ampere's Law. What happens to H
> and B when a blob of material with a different permeablity is placed in
> the region is not clear from the Biot-Savart Law. It seems to create a
> much more complex problem in which the magnetic boundary conditions and
> Ampere's Law or the Biot-Savart Law (now both almost intractable to
> compute) become all coupled together into a horrible system of equations.
The symmetry is ruined. The contours of constant H are
to determine or don't exist.
> Finally, let the toroid be thin in the z dimension so that H is
> relatively uniform over variations in z for a given r. (Does this matter?)
The requirement is axial symmetry. So, you calculate
your perfect 10cm toroid and find that all the non-zero
H is inside the toroid. Then I plop a steel nut down
10 m off axis and ruin your perfect axial symmetry.
Now, the H gets to be non-zero outside the toroid
and you wave your hands and say "well, most of it
is in the toroid".
> I am pretty sure that they are speaking of the peak magnetic field
> strength when I is a sinusoidal current in RMS amperes. But they didn't
> make this clear, and the frustration of having to figure out what they
> meant, as well as having to figure out what a whole bunch of other
> magnetics engineering formulas mean is what has led me to decide to
> ignore most of them and derive them on my own.
usually they say something like this core,
this winding, this many turns, yields this
Oh by the way, mu is not an isotropic scalar, but a
stinking tensor. Mu varies with the direction of the
flux. So even a perfect torrid is a problem unless
the magnetic grain is oriented along the circumference
(you get this with tape wound cores, if you are careful).
Thank you for reading and or replying
If you are one in a million, there are 6000 people just like
Local optimization almost never yields global optimization.
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