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Re: induced emf and eddy currents

If we read Kirchoff's papers, we find out that Kirchoff may well have
understood that Int[E.dL] around a closed loop was not always zero. Also,
that the Sum[I] and any node or junction is not always zero.

I like to teach Kirchoff's Laws inf the following way (especially to my
advanced E&M Physics Majors):

1st => Int[E.dL](arbitrary closed loop) = ZERO, unless it isn't! And,
when it isn't zero, it isn't zero for a very important reason --- namely
that a dPhi/dt has occurred within the loop. That is to say, the total
E-field must be considered if we wish our measurements to match our
calculations, and onlt the E(conservative) will lead to a ZERO net sum.

2nd => Sum[I's](at any point) = ZERO , unless it isn't! And, when it
isn't zero, it isn't zero for a very important reason --- namely that
there has been a dRho/dt of charge at that point. This then leads
naturally and directly to the Continuity Equation.

Besides, I've never met a student yet that doesn't know form instinct or
life experience that the over simplified version of KII (Sum[I's} = ZERO),
must be wrong. Ask any student that you have the following hypothetical
question:

Suppose that you are standing in the doorway of a wall that has a pipe
that appears go through it (you look on the left side of the wall and see
the pipe and you look on the right side of the wall and see what appears
to be just a continuation fo the same pipe).

You now have someone "turn on the water" somewhere and observe that a
guage of the pipe on the left hand side of the wall reads 5 gal/min going
into the wall. On the other hand, a guage on the pipe on the right hand
side of the wall reads 3 gal/min.

KII (Sum[I's} = ZERO) would appear to be violated! But every student that
I have ever asked has always know one or the other or both of all of the
reall possibilities:

1. there is at lease one other pipe in the wall (that we cannot see)
that carries a flow of 2 gal/min;

2. get your mops and buckets, 'cause there is a 2 gal/min leak into
the inside of the wall;

3. some combination of 1&2 to account for the 2 gal/min flow defect.

THEY REALLY KNOW THIS ONE AT A GUT LEVEL!

Try this scenario on your students and I think you'll find that they will
almost all state in english that which you can re-write mathematically on
the board as the Continuity Equation. And since they have "discovered it
themselves, you don't have to convince them that it is correct. I have
found that I have almost no one that fails to remember and write down a
proper continutiy equation after one session like this.


I use similar arguments to help the students understand why they must be
very carefull with their leads when measuring voltages (NOT potentials).


ERTEL SENDS. _____________________
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/ jpe@nadn.navy.mil \
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On Wed, 18 Jun 1997, Chuck Britton wrote:

To help point out the differences between EMF's and voltages we should note
that Kirchhoff's Loop Rule holds for voltage but NOT for EMF's. Asking
students why this is true is a good test of their understanding. (Asking
OURSELVES is a good test of OUR understanding!)

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Chuck Britton Education is what is left when
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