Re: Energy density; the correct one

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

Situation 1. Suppose I hold two equally positively-charged particles, q1 and
q2, a distance r12 apart.  If I keep hold of q1 and release q2, q2 flies off
to a place infinitely far away and gains kinetic energy equal to E2.  I then
release q1, which stays put since q2 is now infinitely far away.  The total
energy of the system is E2.

Situation 2. Suppose I hold two equally positively-charged particles, q1 and
q2, a distance r12 apart.  If I release both particles at the same time,
they fly away from each other.  When they are infinitely far away from each
other, each has an energy E12.  The total energy of the system is 2*E12.

In situation 1, I did no work on either q1 or q2.  I admit that my muscles
converted chemical energy to heat energy in the process of holding onto q1,
but I still did no work *on q1*.  q1's electric field did work on q2.  The
work done by the q1's electric field on q2 equals the kinetic energy gained
by q2, E2.

In situation 2, I did no work on either q1 or q2.  Is E1 equal to 2*E12?

____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301

> -----Original Message-----
> From: David Rutherford [mailto:drutherford@SOFTCOM.NET]
> Sent: Wednesday, September 25, 2002 3:22 AM
> To: PHYS-L@lists.nau.edu
> Subject: Re: Energy density; the correct one
>
>
> Bob LaMontagne wrote:
> > OK - I'll bite - How do you do work on a charge that isn't
> moving - being
> > held in place - where's the displacement needed for the
> usual definition of
> > work?
>
> The conventional way of dealing with this problem is to
> assume that the
> existing charges will just stay where they are while you bring in
> additional charges. That's not going to happen all by itself.
> There must
> be, as I said, the _equivalent_ of work being done on the existing
> charges. If you don't include this, the existing charges will
> go flying
> off to infinity again and you'll never be able to assemble a charge
> distribution. I'm assuming that the distribution can be assembled.
>
> --
> Dave Rutherford
> "New Transformation Equations and the Electric Field Four-vector"
> http://www.softcom.net/users/der555/newtransform.pdf
>
> Applications:
> "4/3 Problem Resolution"
> http://www.softcom.net/users/der555/elecmass.pdf
> "Action-reaction Paradox Resolution"
> http://www.softcom.net/users/der555/actreact.pdf