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In a population of hydrogen nuclei, the associated magnetic moments align with an external magnetic field. Each hydrogen nucleus can be in one of two states: a high energy state (antiparallel) and a low energy state (parallel). What bothers me is the orientation of the magnetic moment vectors. I would assume that the north poles (tips of magnetic moment vectors) tend to move towards the south pole of the external magnetic field. But the opposite, i.e., parallel orientation, is of lower energy (see the picture - taken from http://mriquestions.com/magnetic-dipole-moment.html).

magnetic moment vector <span class=$\mu$ of a nucleus in an external magnetic field B0 taken from http://mriquestions.com/magnetic-dipole-moment.html">

Can anyone explain why this is the case?

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1 Answer 1

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I think what got you confused here is the way we usually learn about the direction of magnetic field lines. The notion that they point from the north to the south pole only applies outside of a e.g. permanent magent. Since the lines have to be closed, they reconnect inside the magnet, but then pointing from south to north.

If you want to think about the orientation in the classical sense that opposite poles attract, think of the external field as generated by a permanent magnet just below where your dipole is. Since the field lines point north to south (we are outside the magnet), the north pole of this magnet must be pointing up, towards your dipole. Now since opposite poles attract, the dipole has the lowest energy orienting its south pole towards the permanent magnet's north, which is exactly the low energy configuration in your picture.

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  • $\begingroup$ Thank you very much for your quick answer. $\endgroup$
    – Laly
    Jan 24, 2020 at 18:51
  • $\begingroup$ Right, the field lines are connected, so outside the magnet they go from N->S, but inside they go from S->N. The magnetic field I have in mind is induced by current through a coil. That means the magnetic field lines inside the coil are directed S->N. If I place a nucleus inside the coil, then - as opposite poles attract each other - the magnetic moment vector should point N->S. (I assume that the magnetic moment vector corresponds to a small magnetic field pointing to its own local north pole. In the image B0 is S->N and mu is S->N, right?) What's wrong about my concept? $\endgroup$
    – Laly
    Jan 24, 2020 at 19:02
  • $\begingroup$ The concept of attraction to south and north pole only makes sense outside a magnet, where these things are clearly defined. In general, it is much more useful to say that magnetic moments align their direction (which, if you want to see it as a magnet, points from south to north) with the direction of the magnetic field lines, whose direction I described in the answer. $\endgroup$
    – noah
    Jan 24, 2020 at 19:30
  • $\begingroup$ You can also see it as: outside the magnet (or coil) the concept in the anwer holds. there is no disruption in the magnetic field lines as you move into the coil, they just curve smoothly into it. They don't twist or curl, nor are they discontinuous. Therefore the moment will show the same behaviour inside the coil as just outside of it, i.e. will not flip around once moved into it. $\endgroup$
    – noah
    Jan 24, 2020 at 19:34
  • $\begingroup$ So does that mean, that in the image, the arrow representing B0 goes from N->S (as between opposite poles of permanent magnet) while the arrow representing the magnetic moment vector points S->N? $\endgroup$
    – Laly
    Jan 24, 2020 at 19:46

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