Michel Jullian wrote:
Right, this is Paul's paradox (he does make sense occasionally ;), so
it seems only the second and third way of looking at things
(potential energy and work of forces) are equivalent in all cases.
Maybe the paradox comes from electric and gravitational fields being
static in nature whereas magnetic field results from a motion?
Something just occurred to me when I read that. A "dipole" made of two
nearby monopoles shows the same effect, and we can build one of those
from electric charges.
So, two electric dipoles will also show increasing field energy as they
draw together.
Hmmm.... This deserves more thought...
Maybe
a full relativistic analysis could reconcile all approaches.
Michel
----- Original Message ----- From: "Stephen A. Lawrence"
<[EMAIL PROTECTED]> To: <vortex-l@eskimo.com> Sent: Friday, February
02, 2007 4:38 AM Subject: Re: [Vo]: electricity question
Michel Jullian wrote:
Paul, Paul, Paul you missed my point again, never mind :)
To go back to your pet theory, since as you said the formulae for
field energy and potential energy are the same, there are in
fact at least three equivalent ways to describe the same thing:
field energy, or potential energy, or work done by the forces.
A minor nit to pick: Potential and field energy may be
interchangeable for electric fields, but apparently not for
magnetic fields. Permanent magnetic dipoles have potential energy =
-mu.B which is not tracked by the total field energy. Case in
point: If the field of one dipole has energy E, then the fields of
two widely separated dipoles have total energy 2E. Let them pull
themselves together until they touch end to end -- the potential
energy drops, but the total field energy increases, to about 4E, as
the two fields overlap almost exactly. (The energy density goes as
field intensity squared, so halving the volume while doubling the
intensity yields a net energy increase of 2x).
So if we include permanent magnets in the picture, it's going to be
awkward to replace PE with field energy everywhere. I think this
may be what led Paul to assert that nobody knows where the energy
comes from in this case.
All in all the third way:
Kinetic energy change = Work done by the forces
seems the most sensible to me as it is universal (functions with
all types of forces), it is not 'potential', and it is also the
most fundamental since fields are defined from forces, not the
other way round as is commonly thought.
How does the work approach fit with your violation theory?
Michel
