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

["Bill Nettles" <bnettles@uu.edu>]

The electrostatic force that you use can only be considered conservative within the system. As soon as you make it external to the system, it is non-conservative for that system. That's because you are ignoring the PE of the system due to the electrostatic field. Also, turning the field on and off is a non-conservative event. It's just like adding and subtracting charges from the system.

Bill Nettles
Union University

> > > John Denker <jsd@av8n.com> 2/19/2008 8:40 pm >>>
On 02/19/2008 04:53 PM, Alfredo Louro wrote:

> > 2) You can change the sum of KE and PE of a system by doing work
> >  with a conservative force
>
> I'm not sure I follow. Could you give an example?

Here's a pair of complimentary examples:

Example 1: Grady force:
*) Electrostatic force is a grady force.
*) Ignore non-electric fields and potentials.  Gravity is ignorable if the
  particle is constrained to move horizontally.
*) Define "the system" to be a charged particle, initially at rest, but
  free to move.
*) Apply an electric field, initially zero, then nonzero, then zero again.
*) The particle picks up a nonzero kinetic energy.  BTW it also
  picks up nonzero momentum.  Energy and momentum were transferred
  across the boundary of "the system".
*) Potential is the same before and after, so the *sum* of KE and PE
  is changed, not just KE at the expense of PE.
*) If you want to get fancy, argue based on symmetry and/or timescales
  that we can arrange that the electrostatic approximation is valid, i.e. 
  magnetic effects can be neglected (subject to mild restrictions).


Example 2: Non-grady force:
  Same as above, but use a betatron field rather than an electrostatic
  field.  Argue that grady electrostatic terms are negligibly small
  compared to non-grady betatron terms.



If that doesn't answer the question, please ask a more-specific question.
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