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Re: [Phys-l] non-conservative --> non-grady ???

Regarding John Denker's capacitor accelerator --

Consider the following geometry
http://www.av8n.com/physics/img48/accelerator.png
and the following method of operation:
As before, the charged particle is deemed "the system".
At time t_A the particle is at location A moving slowly to
the right. The KE is small. The field is off.
At time t_B the particle is at location B. We turn on
the field. This does not affect the particle, because
it is outside the capacitor, where the field strength
is small, and can be made arbitrarily small by suitable
engineering. Any /magnetic/ effects are doubly negligible,
firstly because the field is small, and secondly because
the particle is on the axis of symmetry ... which /direction/
would the magnetic force have????
At time t_C the particle is at location C. It is being
vigorously accelerated by the field.
At time t_D we turn off the field. This has no effect on
the particle. The particle retains its large KE.
Magnetic effects are doubly negligible.
At time t_E we observe the potential energy to be the same
as at t_A, and the KE to be much larger.

At no time was the particle exposed to a non-grady field of
any significance. Yet energy was transferred across the
boundary of the system.



How would the analysis be different if instead of having an electric field
accelerate a charge we had a fast moving conveyor belt between the plates
that grabs onto a crate that's delivered through the hole on the left so
that friction does the work of getting the crate up to exit speed?

I'm imagining the belt going so fast that the crate is slipping the whole
while as it travels in the area between the plates. What I'm after is what
the difference is when the force doing the acceleration is a nonconservative
one like friction compared to a conservative one like an electrostatic
force.

Steve Highland
Duluth MN