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Re: "Faraday's Disk" which started it all



Well, it's taken us a while, hasn't it, but we've finished (?) up with
some really sound physics presented with flair.
Thanks, Bob and also William for starting it and keeping on niggling
away so that we lurkers were able to improve our understanding.
Brian McInnes
----------
From: Bob Sciamanda <trebor@VELOCITY.NET>
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: "Faraday's Disk" which started it all
Date: Thu, 1 Jul 1999 12:48 PM


William and Robert:
(Please allow me a two for one shot :)

Two very different velocities V are being used here.

1) In F = qVxB, V is the velocity of the particle whose charge is q; B is
the magnetic field (of some source) measured at the location of q; F is the
force which q experiences due to its interaction with the field B. All of
these four quantities are measured by an observer in a given inertial frame.
In particular, V is simply the velocity of the charged particle in this
frame. (Note that the kinematical status of the source of B is not
explicitly relevant - the local [at q] value of its field B says everything
about its magnetic force on q - this is the essential usefulness of a field
theory - indeed B may be the net field of numerous sources.)

2) Special Relativity asserts that this equation can be used in any inertial
frame, exactly as stated above - none of the infinitely numerous inertial
frames is to be preferred. The same is asserted about all of the equations
of Maxwellian E&M, including the relations giving fields in terms of their
sources, etc. If Maxwellian E&M is correct it can be applied in any
inertial frame, without any reference to the velocity of that frame relative
to anything. From this assertion, relativity produces the transformation
equations relating the values of the quantities q,V,E,B, etc. as measured in
DIFFERENT inertial frames. In such a transformation equation U, the
RELATIVE VELOCITY OF THE TWO FRAMES, is the specifying parameter.

As an example: if in frame S there exists a uniform magnetic field B; then
in a second frame S', traveling at a velocity U (as measured in S) in a
direction perpendicular to B, a magnetic field B'=B and an electric field
E'=UxB will be measured. Neither frame is more correct than the other.
There will also be different source configurations in each frame, and in
each frame the sources will account for the observed fields, by the same
"laws of physics", which connect the values of quantities as measured in any
SINGLE frame.

Confusion often results when the second frame is chosen to be the rest frame
of a charge q which has a velocity V in the first frame. In this case V=U
and the interpretation of equations can invite mushy thinking.
Respectable texts are not immune from inviting this malady.

Very important NOTE:
Note that relativity does not, of itself, do any physics for you. You must
define the problem and solve it in some inertial frame. Relativity will
then tell you what measurements will result in any other inertial frame.
For example, it is the task of condensed matter physics (or just experiment)
to tell us the charge and current configurations of a current carrying wire
in some frame, eg. in the rest frame of the wire/battery setup. If you find
that the wire is neutral in this frame, relativity will tell you that there
is a non-zero linear charge density in certain other frames, etc. Again, if
you find that in the rest frame of a disc magnet (even if its on a space
ship) there is no E field, relativity will show you an E' field (and an
electrical polarization P' in the magnet) in some other frames.

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor