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

How do you "turn off" the field. Certainly just opening the switch
doesn't do it. Do you discharge the capacitor somehow? What happens to
all that energy? Isn't KE given to the capacitor just due to simple
momentum conservation? I assume the switch is radio controlled - or is
the operator and earth part of the system? I'm just trying to see if you
can actually do your thought experiment in practice.

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Wednesday, February 20, 2008 1:10 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] non-conservative --> non-grady ???

On 02/19/2008 08:28 PM, LaMontagne, Bob wrote:
Isn't the changing electric flux introducing a non-conservative
magnetic interaction that the charged particle interacts with once
it
starts to move? Perhaps I'm not visualizing this in the sense that
you meant, but it doesn't seem to be purely conservative.

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.


==========

On 02/19/2008 08:36 PM, Alfredo Louro wrote:
But surely the forces can't be conservative, if they're time
dependent?

The field in my particle accelerator is /piecewise/ time-independent.
-- During the entire time that the particle sees a non-negligible
field,
the field is time-independent.
-- During the times that the field is changing, its effect on the
particle
is negligible.


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

This business of being able to do work using only grady force-fields
is important in many real-world situations. Consider for example
one of the first physics demos many people encounter: contact
electrification, commonly called "static electricity". The typical
contact electrification scenario involves only forces that are
the gradient of some potential, yet you can do quite a bit of work
with such forces.

For that matter, water is held in a ladle essentially by grady
forces, yet you can do work on the water, ladling it from a
lower bucket to a higher bucket.

I chose the less-common example of the capacitive particle accelerator
because it is amenable to precise analysis. In contrast, rigorous
analysis of contact electrification is a more demanding task. But
even that is doable; if you're interested, check out
http://www.av8n.com/physics/contact-electrification.htm

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