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? Maybe a full relativistic analysis could reconcile all approaches. Michel ----- Original Message ----- From: "Stephen A. Lawrence" <[EMAIL PROTECTED]> To: <[email protected]> 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 >
