Re: Energy density; the correct one

["Carl E. Mungan" <mungan@USNA.EDU>]

John Mallinckrodt wrote:

>  >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.
>
> Hmm.  This may lead to some dubious energy accounting.  I'd be more
> comfortable saying that the "excess" electric field energy of the
> initial *system* was the source of q2's ultimate kinetic energy.

I like the above example and believe it's worth thinking about in
connection with work and energy. Here's an analogous gravitational
case:

I drop a ball from rest from some height. (System=ball.) It gains KE.
Why? Well, because the earth pulled it downward while the ball was
moving downward and hence did positive work on it.

But work is an energy transfer from one object to another, right?
Therefore since the ball (adiabatically) gained energy, the earth
must have lost energy....

I think this is what John may mean by dubious energy accounting. The
problem is we forgot to include the gravitational field in our story;
it is the "third object" and it can gain/lose energy. Carl
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/