Re: induced emf

["Prof. John P. Ertel (wizard)" <jpe@nadn.navy.mil>]

Ludwik is of course correct --- one cannot directly examine the dB
produced by son IdL.  The differential form cannot be verified as such.
Also, the concept of a differential current element is a mathematical
abstraction --- but is it?  Isn't what we think of as a point charge
moving with a some speed the same as a differential current element?  And,
by the way, how do we verify that it is really a point charge?

We might as well eschew the differential form of the electric field, dE,
produced by a dQ that is part of a body of charge.  But we do not!  We
regularly consider the differential form of the electric field as reality
because the differential source is thought of as like a point charge which
we consider as reality.  BTW: How real is a thing which has ZERO radius?
Of course, symmetry is our friend here.  From symmetry, we can easily
argue the any spherically symmetric charge distribution acts like a point
charge, and the spherical charge distribution (of non ZERO radius) is a
reality.

I mention this only because I have always been concerned about the human
willingness to categorize things as real or not according to our limited
ability to observe.  I've yet to see an individual atom, let alone an
electron, but I'm sure that they exist.  Oh sure, I cannot well describe
their physical extent.  I have to infer it from scattering data and then
we have some intriguing uncertainties.  But if I want to observe a "real
physical ball" (such as a ping-pong ball) that is beyond my physical
reach, I must also estimate its size "from scattering data".

Without trying to become too philosophical, I would ask, "What's real and
what is not?!"

For me, the main reason why I would prefer to deal with the differential
form of almost all "laws" is that we always lose information when we are
forced (as we many times are) to move to the integral expression.  I'll
give up detail when its is unimportant or if I have to, but grudgingly
none-the-less.

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

On Fri, 20 Jun 1997, LUDWIK KOWALSKI wrote:

> Why should we accept the idea that laws in the differential form are always
> more fundamental than laws which describe integral effects. In most cases
> experimentally verifiable relations are integral.
>
> Consider the Biot-Savart formula (giving dB produced by a selected current 
> element I*dL at any location). This simple relation can be used to dervive
> (by integration) the magnetic field produced by a wire of arbitrary shape.
> The opposite was much more difficult; it had to be guessed. Yes, from strictly 
> mathematical point of view the "fundamental" nature of the B-S formula is 
> quite obvious. But the formula can never be directly verified (I am referring 
> to wires, not particles) because a single current element is an abstraction 
> we can not produce in a laboratory. Measuring dB produced by single charged 
> particles is not possible in common student labs.
>
> Why should the non-directly-verifiable relations be considered as "more 
> fundamental" from the philosophical point of view? Why shouldn't we say that 
> "what students find through measurements is more fundamental than what they 
> must guess-and-verify"? Aren't we trying to make physics as difficult as it 
> can possibly be? I know that there are many definitions of "simplicity" but
> some are better than others. And what was simple to Feynman is not
always 
> simple to me.
>                                                Ludwik Kowalski

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