Michel Jullian wrote:
> so it seems only the second and third way of looking at things
(potential energy and work of forces) are equivalent in all cases.
Bingo!
Stephen A. Lawrence wrote:
> 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).
Exactly, and hence the main point of this thread. This was discussed
early on in the thread, but was derailed by face saving attempts. :-(
Two electro-magnets or current-loops demonstrate where the energy comes
from.
> 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.
[snip]
Amen! Two attracted current-loops moving toward each other induce an
opposing voltage on the current-loops, which removes energy from the
source that maintains the current. Here's the theory -->
It requires energy to create an electron and positron. Therefore we
know the electron contains energy. Energy is moving from the electron
to KE with an increase in net magnetic field as two attracted magnetic
dipole moments accelerate toward each other. I firmly believe such
energy comes from the electron. This is simply moving energy. This also
works in the case E-fields or even gravity fields. Two attracted
opposite charges accelerating toward each other gain KE. Such KE comes
from the E-field-- the net E-field decreases as they move closer.
Similarly, two oppositely charged particles require energy when forced
together. Such energy goes into a net increase in E-field.
Here's another interesting aspect of the theory. Consider an electron
and positron accelerating toward each other. The net E-fields decrease
as they approach, thereby adding KE. Furthermore, the magnetic dipole
moments of both particles tend to align on average. We know that when
two current-loops (magnetic dipole moments) move toward each other in
alignment that energy is moving from the current source to KE.
Similarly, I believe energy is moving from the two particles to KE and
radiation as they move toward each other in alignment. Interestingly
enough the two particles are considered annihilated when they reach
certain proximity. It seems likely energy is being drained from the two
particles as they move toward each other until such a point they become
unstable, in which the two particles disrupt their internal structures.
Given the above, it appears energy is removed from the electron as it
accelerates. Also energy is added to the electron as it decelerates.
This lead to other thoughts such as perhaps what would happen if we
accelerate the electron to c. This could possibly drain the electron.
Initially I thought this could annihilate the electron, but now I
question if anything would happen to such electron. Such acceleration
may not change the internal structure of the electron. Therefore, the
electron could simply slow down and remain intact. It appears it
requires another particle to drain and disrupt the internal electron
structure.
Regards,
Paul Lowrance
