Natural Science Forum / Physics / General Physics / June 2007

What is the electric field near a rotating wire section rotating like a
baton? (Let's say, close to the relevant side and axis of a slowly rotating
rectangular current loop.)  I am wondering why the use of some valid field
rules conflicts with what we expect from this apparently reasonable
assumption: to pretend that each piece of the wire "projected" the effect
it's magnetic field would have, if the segment is considered separate and
moving in a straight line at its velocity.  The Maxwell equation curl E =
- @B/@t doesn't give the E field directly. We can use the A field (magnetic
vector potential) instead, which is parallel to the current producing it and
decays as 1/r.  The electric field projected from sources can be given as:

E = - Del phi - @A/@t

If we figure that the net phi stays neutral, then the A vector would swing
around with the rotating wire.  The derivative produces an E field
perpendicular to the wire, "trailing" the wire's rotation per the current
direction.  That seems to fit in with what we'd expect if the entire loop
was imagined composed instead of an equivalent set of parallel sheets of N
and S magnetic charge, and we took the electric field from their motion (the
mirror image in effect of the magnetic field from moving electric charges.)
Furthermore, the A field of a magnetic dipole is lines circulating around
the direction of the dipole, the loop can be considered a mass of parallel
dipoles, and so when it rotates we expect the same result.

However, suppose we consider the magnetic fields from each segment of the
rotating wire (see drawing below of the wire, with O and X for coming toward
or away not current, which is arrows.) The point of interest is "*" which
should be along the axis if font cooperates.

          |
          *
          |
          |
O----->---->---->----X
          |
          |
          |
          |
   axis of rotation

So, if I am a bit away from the center of, perpendicular to the plane of
rotation, each segments' B field vector moves parallel to me.  Also,
segments on each side move in opposite directions anyway.  Looked at this
way, there should not be any induced E field.

Well, the conventional A field and dipole field argument should be right,
but I still don't understand why the two concepts don't agree.  The idea of
using the field from each moving segment separately seems like it should
work (but only "has to" for consistency if the whole thing moves together
...)  I want to know why it doesn't work, in terms of how parts of wires
project their fields, the oddities of rotation in electromagnetism, etc.  It
might also tie into, is there any way to tell the difference from a "real
magnet" and a solenoid, not counting stuff like power use/resistance etc.
I am waiting on replies elsewhere, but meanwhile,
this could make an interesting discussion here. Thanks.