Re: [Phys-l] Magnetic force and work

["Snyder, Tom" <Tom.Snyder@llcc.edu>]

John,

1)  If the field has no azimuthal component, then the divergence expressed in cylindrical coordinates is

div(B) = B_r/r  +  dB_r/dr  + dB_x/dx

Here r is the radial distance from the x-axis.  If the last term is zero, then we can still satisfy div(B) = 0 by having B_r fall off inversely proportional to r for values of r near R (the radius of the ring). [In my example we don't need to require dB_x/dx to be zero, so we actually have some extra freedom to play with in order to satisfy div(B)=0.]

2)  We can assume the ring is a dielectric, such as a thin plastic rod bent into a circle.  We imagine electric charge to be uniformly spread around the ring. 

3)  I'm not following your comment about the cyclotron.

The link on railguns seems to imply that it's the Lorentz force (magnetic force) that directly propels the projectile.  This would be misleading if interpreted as saying that the magnetic force does the work on the projectile.  The magnetic force acts on the moving charge carriers in the projectile and the magnetic force does zero work on any of these charges.


________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of John Denker
Sent: Fri 3/24/2006 12:48 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Magnetic force and work



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

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l