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Re: Inductance



At 09:59 PM 4/12/00 -0700, Leigh Palmer wrote:

In my opinion there is every reason to resist the flux-based definition.

I wouldn't have said "every" reason. There are flux-versus-current
equations that have their uses; for example see item (b) below.

Also keep in mind that flux is the canonical variable that is dynamically
conjugate to charge, so in a really unfamiliar and/or tricky situation,
formulating things in terms of charge and flux is often the best way to
capture the correct physics. (Whether it captures the conventional
definition of inductance is an iffier question.)

In a multi-turn inductor, one also must decide whether to use "phi sub N"
(the flux linking a given turn) or capital Phi = sum_over_turns{phi sub N}
= the total linking flux. The latter is often more physical, but it is
somewhat unconventional and converting back and forth is a perennial source
of confusion. (Indeed an hour ago I wrote Phi when I should have written
phi.)-:

As it turns out the flux-based formula is the result of applying the
real definition to a linear inductor with geometry and electrical
characteristics which do not vary in time.

I wouldn't have said that, either, for a couple of reasons.

a) If the inductance is changing, then neither
V = L d(I)/dt (1)
nor
phi = L/N I (2)
is a reliable guide to what is going on. You need to know more about
what's changing and what's being held constant.

b) If the situation is nonlinear, then equation (1) can be taken as a
definition of the small-signal inductance, but then it doesn't tell the
whole story; it doesn't capture the important physics. You need to know
much more. It is quite likely that it is easier to capture the physics in
an equation of the form
phi = F(I) (3)
[which is a generalization of equation (2)] rather than in an equation of
the form
V = f(dI/dt) (4)
[which is a generalization of equation (1)].



The "swinging choke" comes to mind immediately, of course,
but astrophysical examples abound as well.

The term "swinging choke" is radio-engineering jargon. Check out
http://www.bigcountry.com/w5ami/AMPX/64.html

As an even more common example, there is almost certainly a saturable
transformer regulating the voltage to your home.


While I'm railing against these neosacred cows, let me also deplore the
use of the word "potential (meaning electrical potential) in this or
any other time dependent application. I like to firmly associate the
terms "potential" and "time invariant" with one another. Perhaps "emf"
would be a better choice?

EMF is vastly better than "potential". But EMF isn't really a force. I
generally use the term voltage and leave it at that.