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Re: Inductance



Points of discussion for John, Leigh and others


The voltage V across an inductor is given by
V = L d(I)/dt (1)

Where L is the inductance and is assumed to be constant.
This expression
is the definition of inductance, and makes sense for
inductors of nonideal
as well as ideal shape.

I'd have to ask where does this definition come from? Since to be useful as
a definition for calculating L (not measuring L) you need to know how to
calculate V. Its a bit of a chicken and egg situation. I believe the answer
is that it comes from a flux calculation; i.e. noting that for some surface
whose boundary has a well defined current, and allowing for the possibility
and existence of other currents in the "universe"

Flux = L*I + SUM of M_j*I_j

i.e. noting that the flux is linear in the currents where L and the M_j's
are constants. (This is essentially a Biot-Savart law statement). One
differentiates wrt time and the left l.h.s. is then the induced emf (from
Faraday's statements) in that boundary. And then definition (1) more or
less follows. So it strikes me that definition (1) is flux based.

I believe (perhaps incorrectly) that that is the allusion John is making in
his following post where he states:

"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.)"

Asterik emphasis is mine in the above quote.

Comments John or Leigh, or others?

Interesting that this just came up on the list, I just hit this topic in my
intro course.

Joel Rauber