1. At the end of my last message I *should* have written ...
... it is useful to represent the collective effect of collisions
through a viscous-type -b(v-u) force where u is the velocity of
the medium through which the conduction electrons are flowing and
b is the product of the charge carrier mass and a representative
"collision frequency."
Thus, in the lab frame, we do indeed write
F = qE + qvxB - b(v-u)
with the last term accounting for the effects of resistance.
To be specific, in Ludwik's problem (with a 0.1 m long 1 ohm rod
moving at 10 m/s along a U-shaped frame with a total resistance of
3 ohms) we would find within the rod*
E = 7.5 V/m opposite the direction of current flow,
vxB = 10.0 V/m in the direction of current flow,
-b(v-u)/q = 2.5 V/m opposite the direction of current flow.
Thus, F = 0 and, as a result, v is constant.
*neglecting small quantities associated with the Hall effect that
are in turn associated with the small difference between v and u.
2. I wonder why my previous post generated all of those ugly ASCII
codes toward the end? Will this one do the same? I haven't done
anything that differs from my usual procedures.