Re: EM Induction - A conceptual question

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

"Fakhruddin, Hasanbhai" wrote:

> Imagine a circular loop of wire of radius R.  A uniform
> magnetic field is distributed perpendicular to its surface
> and confined to a concentric circle of radius r < R.

How can such "beam of B lines" be produced? I suppose
a long solenoid whose radius is r could do it, approximately.
Or perhaps it is a toroid (with an iron core) whose size is
so large that B is locally uniform. In such cases, a changing
B is caused by a changing current. The question is "how
can a change in one current produce a change in another
current at some distance away?" The concept of B was
invented to eliminate the question. We say

delta(I1) --> delta(B) --> delta(emf) --> delta(I2)

But in Hasan's illustration the field B is not in contact
with the loop in which the emf is induced. In this case
the field B does not help us to eliminate the old "action
without touching" dilemma. Perhaps such action should
simply be accepted as an experimental fact.

But then, one may ask, "why do we need B?" My answer
would be "to simplify calculations." Expressing delta(I2)
in terms of delta(I1) directly would involve the double
cross product. It is easier to calculate delta(B) from
delta(I1) first, then calculate delta(emf) from delta(B) and,
finally, calculate delta(I2) from delta(emf). OK, replace t
he delta(B) by the delta(FLUX), if you wish.
Ludwik Kowalski

>