Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: induced emf again



I will read the description of the gedanken experiment
of Feynman (see John's message below) and see how
easy it would be to turn it into a real experiment. But
here is another suggestion, illustrated it numerically.

Suppose the rod whose length is 0.1 m is moved at
v=10 m/s in a uniform field of 1T. In this case the
emf=1 volt. Suppose the rod resistance is 1 ohms
while the resistance if the "rail," on which it slides,
is 3 ohms. The expected i1=333 mA is larger than
i2=250 mA which would flow if the emf was
distributed ("working" against the total resistance
of 4 ohms rather than against 3 ohms only).

I think that the one ohm resistance of the rod does
not contribute to the current because motional emf
(voltage causing the current) exists between its end
points. Otherwise rod's resistance would act as it
were an internal resistance of a battery and i1 would
be 250 mA. Note that the effect of the magnetic field
produced by a current is ignored; it would not be
significant in this case.
Ludwik Kowalski
***************************
"John S. Denker" wrote:

Ludwik Kowalski wrote:

The origin of my misconception is probably rooted in
the rule according to which "the way in which the flux
changes is not at all important, it can be a stationary B
but changing area, or it can be a constant area but
changing B."

I would say the misconception is to think that the
flux "rule" is a hard-and-fast rule. When in doubt,
use the Maxwell equations. The flux "rule" is not
a Maxwell equation. It is a consequence of the Maxwell
equations _under certain conditions_.

But Faynman argues that two ways of
changing the flux result in two different phenomena.
Right or wrong? I wish I could refer to an experimental
verification of this theoretical claim.

You could build the apparatus in Feynman's figure
17-2 and figure 17-3. Use a pull-string around the
shaft in figure 17-2 to spin the disk. And in figure
17-3, you don't even need the rocking sectors; you
can make the same point with alligator clips or switches:

____ \______
| A |
| |
| |
|___ \______|
| B |
| |
| |
|____M______|

where M denotes a galvanometer meter.

Take turns opening switch A and closing switch B, then
vice versa. It changes the amount of flux in the loop,
but it doesn't induce any voltage.

Some people are content to treat these figures as
Gedankenexperiments: just analyze them using the Maxwell
equations and all becomes clear. But you can implement
them as real experiments, too.

Why are the "two distinct phenomena" not recognized
in our introductary textbooks?

Because life is too short. The best thing to do in a truly
introductory course is teach the reliable way to analyze things
(Maxwell equations in this case) and not bother with the
innumerable unreliable ways to analyze things.

Why don't we have two
distinct names for two distinct phenomena?

We do, sort of. One of them is called E and the other is
called v cross B.

How come that both emfs can be
calculated by the same formula? Only a coincidance?

Feynman called it a coincidence. If Fluck's rule were
true in general, it would be worth figuring out why.
But since it is true in a few special cases and not true in
other cases, I'm not highly motivated to figure out what
the true cases have in common. Maybe nothing.

Sometimes you can construct cases where E in one frame
turns out to be v cross B in another frame, in which case
I wouldn't call it a coincidence. But this isn't the general
case and you shouldn't get too excited about it. If you're
serious about using multiple frames to discuss flux lines
or any other EM phenomena, you should be using tensors, not
E-vectors and/or B-vectors and/or flux-lines separately.