Re: [Phys-l] Magnetic force and work

[John Denker <jsd@av8n.com>]

Snyder, Tom wrote:

> Take a circular ring with a net positive charge uniformly spread around
> the ring. Let the ring be rotating about an axis through the center of the
> ring  and perpendicular to the plane of the ring.  Call this the x-axis.  Now
> add a time-independent magnetic field that has a radially outward
> component at each element of the ring (as well as perhaps a component
> parallel to the x-axis).  By radial I mean perpendicular to the x-axis.
> Such a field could be produced, for example, by a bar magnet placed along the
> x-axis at some distance from the center of the ring with the north pole
> closer to ring.  However, to make the model simple, I imagine that the
> radial component of the magnetic field is independent of x.

1) A B-field radially outward independent of x violates the Maxwell
  equation del dot B = 0.

2) I assume the ring is not a conductor.  To ensure that the charges
  rotate with the ring, the ring must be nonconducting, or at least
  piecewise nonconducting.  Isolated metal beads on an insulating
  carrier might do the job.

3) Isn't this just a thinly-disguised version of the cyclotron orbit
  problem ... with a slightly different effective mass in the X direction
  than in the theta direction?

==================================

While we're on the general topic, note that there is a vast literature
on railguns and other electromagnetic guns (amateur and professional).
  http://en.wikipedia.org/wiki/Railgun
  http://www.google.com/search?q=railgun