Re: Inductance

[John Denker <jsd@MONMOUTH.COM>]

At 08:42 PM 4/12/00 -0500, Lemmerhirt, Fred wrote:
> By habit, I define the inductance of a circuit element as the ratio of  "V
> sub L"  across that element to the rate of change of current in it,  where
> "V sub L"  is the potential difference that appears only when the current is
> changing.  But lately I've noticed that currently popular textbooks tend to
> define inductance as number of turns times flux divided by current.  Is
> there some reason to prefer this "flux-based" definition?


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.

The flux Phi is given by
        Phi = L/N I             (2)

Strictly speaking, it only makes sense to speak of "the" flux in cases
where there is the same flux in each turn of the inductor.  This could
happen in various special cases, including a single-turn inductor, an
infinite solenoidal inductor, or a perfect toroidal inductor.  More
generally, we could interpret Phi to be the flux in an "average typical" turn.

If equation (2) is meaningful at all, it is equivalent to equation (1)
because the voltage per turn is guaranteed to be
        V/N = d(Phi)/dt

(I believe Prof. Maxwell had something to say about that.)

==================

BTW, I have various quibbles with the details of the question as quoted
above.

For one thing the voltage across the inductor is *not* a potential.  It's a
non-potential voltage.  By definition of "potential" (electrical potential
or otherwise), the potential difference between point A and point B has a
value independent of the path taken from A to B, which is most definitely
not the case here.