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## Main Question or Discussion Point

**simple magnetic dipole moment with impossible field lines? clueless.**

Hello,

I'm taking a first year university course in electromagnetism. At a certain point we came upon the torque on a current loop in a uniform magnetic field. There we introduced the magnetic dipole moment [tex]\overline{\mu} = I\overline{A}[/tex] with I the current through the loop and A the surface in between the conductors that form the loop (so I suppose this definition is a special 2D-case). Then the torque on the loop turned out (surprisingly enough always) to be [tex]\overline{\tau} = \overline{\mu} \times \overline{B}[/tex].

Now in that whole discussion, the concept of magnetic dipole moment seemed to be something purely geometrical. Yet in the exercises there was vaguely mentioned that if "something" has a magnetic dipole moment, you can look at it as a little magnet, with the magnetic dipole moment vector pointing from N to S (the poles). Okay, I figured this comparison with a magnet was made because it

*behaved*like a magnet (i.e. it alligns itself in a magnetic field). But after some online searching, I found "something" with a magnetic dipole moment actually "has" magnetic field lines, like an actual magnet. How does this suddenly arise out of the previous geometrical-like definition and role of this quantity? Was it silly of me to assume there could be something that behaved like a magnet but didn't have magnetic field lines? It does sound silly in sé.

If the confusion stopped there, it would be alright. But in the next chapter we saw the other elementary result that an electric circuit is a source of magnetic field lines. Now I figured, they must be the same field lines (although that would also be odd, having seen they exist before seeing they exist in the chapter devoted to it). But it turns out --after drawing those

*latter*field lines for a random circular loop, i.e. the magnetic field originating from the current itself -- that they're exactly opposite to the field lines associated with the magnetic dipole moment of the object.

Are they connected? Is one negligible compared to the other? How do you even calculate the field lines due to the geometric-like magnetic dipole moment? Is my confusion a fair one, because I must say I'm getting the feeling I'm lacking a whole lot of understanding.

A genuine thanks to all helpers,

mr. vodka

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