----- Original Message ----- From: "Stephen A. Lawrence" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Thursday, January 25, 2007 2:29 PM Subject: Re: [Vo]: Energy *Violations* using *standard* physics
> > > Michel Jullian wrote: >>>>> a violation of energy conservation? No. Electric potential >>>>> energy is decreasing somewhere, I'll let you find where :) >> ... >>> ...We want to know, lol! :-) >> >> Oops I have found in the meantime that my initial explanation was >> wrong, so it's just as well I kept it to myself ;-) >> >> Electric potential energy has nothing to do with the matter as I >> realized (my apologies for the misleading hint). Still it seemed >> obvious to me that _some_ potential energy had to be decreasing, >> since it takes work to bring the dipoles back to their non-aligned >> initial state. Same reasoning as in the non-rotating case where >> magnets are just attracted to each other, similar to a mass falling >> off a table as previously mentioned by Stephen. This led me to >> Googling "magnetic potential energy", and bingo, there is such a >> thing, and it decreases all right when magnetic dipoles align! > > Yes, I knew that. In fact the formula which you quoted below, > > -mu <dot> B > > applies to linear potential energy as well, which the authors apparently > didn't mention. A dipole in a nonuniform field feels a linear force > which is equal to > > gradient(mu <dot> B) It makes sense. > > and in any field it feels a torque which is > > mu <cross> B > > and these are easily seen to be the negatives of the gradient of the > potential and partial of the potential with respect to the dipole angle, > respectively. > > I actually said this 'way back before the beginning of this discussion, > and again part way through... Sorry I hadn't followed more closely the discussions, it would have saved me reinventing the wheel :) The set of formulae you quote above should be complete enough for any derivations or simulations Paul or others may have in mind. Michel
