Energy of a magnetic dipole in an external B field

1. Mar 17, 2010

kof9595995

As in Feynman's lecture on physics vol 2, he showed that the "true energy" of a magnetic dipole(current loop) in an external B field is m*B, not -m*B. Basically the argument is if you want to pull a current loop from infinity to the final position, you must do extra work to keep the current in the loop constant. If you take this energy into account, the total energy will be m*B.
But in statistical mechanics of magnetization, if we use U=m*B instead of -m*B, we will get the opposite results,for example, we will get that the higher the temperature is, the easier to magnetize a material, which is obviously wrong.
How should I explain this?

2. Mar 18, 2010

Meir Achuz

The reason is (as RF said) that twice as much energy must be provided to a current loop to keep the current constant while it is moved. Although U=+m*B for a current loop, the force on the loop is given by F=+dU/dx so the force on the loop is the same on a permanent dipole. For a permanent dipole, U=-m*B, and F=-dU/dt, giving the same formula for the force. The magnetization in ferromagnetic materials is due to correlated electron spins and not current loops, which is why U=-m*B is apprlpriate.

3. Mar 21, 2010

kof9595995

it makes sense, thanks.