Re: [Phys-l] Magnetic force and work

[John Denker <jsd@av8n.com>]

Snyder, Tom wrote:
> 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). 

I stand corrected.

It would be an interesting exercise to design the pole-pieces
to produce such a field.  The pole-pieces would definitely not
have a shape independent of x.

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

A cyclotron orbit results when a point charge moves in a field that
is everywhere perpendicular to the direction of motion.

Standard case: motion in the xy plane.
Present case:  motion in the rx cylinder.  Unroll the cylinder and
you're back to the standard case.