Potential Energy for magnetic dipole

[richard7893]

I am not understanding why the potential energy (U) for a magnetic dipole is at it's maximum when the magnetic dipole moment is antiparallel to the magnetic field (B), why U is at it's minimum when the magnetic dipole moment and B are parallel, and why U is zero when B and the magnetic dipole moment are perpendicular. To me it seems that U would be greatest when the magnetic dipole moment and B are perpendicular because when the dipole is in this position it seems it would have the most potential to rotate (because this is the position in which torque is maximal). And it seems to me U would be zero when the dipole moment is parallel or antiparallel to B because when the dipole is in this position there is no potential for the dipole to rotate, the torque is zero when the dipole is at the positions. I'm having a hard time following the discussion going on in my textbook about this.

 

[Astronuc]

Is is clear that the potential energy U(θ) of a magnetic dipole moment in a magnetic field is given by

U(θ) = μ • B, where μ is the magnetic moment, B, is the magnetic flux density, and θ is the angle between the vectors μ and B?

Ref:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magpot.html
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html