George Holz wrote:
Stephen A. Lawrence wrote:
The E and B fields together form a rank 2 tensor (the "Faraday"
tensor). The application of that tensor to a charged particle's
4-velocity yields the 4-force on that particle due to the EM field.
Changing FoR changes the components of the Faraday tensor but doesn't
change the effect it has on a particular object.
This seems like a correct way of looking at the problem.
Aren't you agreeing with my original point that the
statement "magnetic fields never do work" is really not
helpful in understanding electromagnetic forces.
In general I would both agree and disagree with this statement. It
doesn't usually help in getting the "big picture" but it's a worthwhile
point to keep in the back of your mind, just as a point of reference; if
you're assuming you're doing work as a result of a B field acting on
charges then something's probably wrong.
In commercial finite element analysis software
forces are commonly calculated by using changes
in magnetic field energy with position without any
reference to electric fields. Do we need to change the
way engineers think about these useful techniques.
No, of course not -- field energy's E^2+B^2, up to a scale factor, and
ExB tells you where it's going. I've got no beef with that.
So where does the energy come from? Do you agree with
my statement that it comes from both the ring and the dipole
or do you say it all comes from the ring.
Every time I start thinking about the inertial mass of an electron I get
a headache.
In this case, the energy was put in by spinning up the ring to start
with, and that's the energy we get back out. Whether it resided in the
magnetic field of the ring while the ring was spinning, or in the
inertia of the ring itself, is something which is beyond me just now
(and luckily, for this problem it doesn't really make a difference...).
Here's another good one: Does a free-falling charge radiate?
George Holz
Varitronics Systems
