From: Chris Carlen
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Subject: Re: Problem with magnetic boundary conditions
Date: Fri, 13 Dec 2002 19:03:00 GMT
NNTP-Posting-Date: Fri, 13 Dec 2002 11:03:00 PST
John Woodgate wrote:
> Consider the magnetic arrangement as analogous to a current source
> feeding two resistors in series, one low value (core piece) and one high
> value (air path). The voltages across the resistors divide the total
> voltage in such a way as to achieve the current match at the junction
> between the resistors.
> Note that this is a 'gyrated' analogy, in which current maps induction
> (B) and voltage maps magnetic field (H). In the magnetic case, the total
> available H divides across the core and the air path so as to keep B
> constant at the interface. This concept is usually studied in the
> configuration of an air-gapped core, in which it's a bit easier to
> conceive of the division of H between core and gap.
This is a good analogy for understanding the fact that Bn1=Bn2, which
stems from div B_vec=0, Gauss' Law for magnetostatics.
My problem is that the Biot-Savart law which is used to calculate
magnetic field strength H at an arbitrary point in space due to the
current flowing in a conductor, pays no attention to the permeability of
the medium, and thus it does not lead to the conclusion that there is a
step discontinuity in the normal component of H crossing the boundary.
I can understand arguing from the starting point of B, that H must go as
u1 H1n = u2 H2n, but the Biot Savart Law says that H is continuous. I
think. Unfortunately the calculations using the Biot-Savart law are
tedious, and I won't have time to do more exploratory experiments with
this until next week, after my final exam. Fortunately that won't
involve being able to understand such subtleties as this.
Thanks for the input. I hope to provide more feedback on this later.
Christopher R. Carlen
Suse 8.1 Linux 2.4.19