Current loop and direction ambiguity of the magnetic moment Consider a circular loop in the XY-plane which carries a current $I$. Then it behaves as a magnetic dipole with moment $\textbf{m}=I\int d\textbf{S}$  where $\int d\textbf{S}$ is the area of the loop and $\int d\textbf{S}$ determines the direction of the moment. Now the area can have two directions: either $+\hat z$ or $-\hat{z}$. Does it mean that the direction of the magnetic moment is also ambiguous? 
 A: The convention is that the direction of the magnetic dipole is determined from the direction of the current using the right hand rule.  For example, looking down on a loop with a clockwise current means that the magnetic moment is downwards.
A: Ambiguous is the direction of the magnetic field lines. Somehow ambiguous is the direction of the electric current too because there are a technical direction from plus to minus or the real direction of the negative charged electrons from minus to plus. So one has to use the right hand rule or the left hand rule.
More important is the fact that - if the directions are defined unambiguously - the direction of the magnetic field is always the same. This has to do with the intrinsic properties of the involved electrons. Electrons have a magnetic dipole moment and a related intrinsic spin. The spins of accelerated electrons - like in a current carrying coil - will be aligned and by this the magnetic dipole moments of the electrons get aligned too (the axis of the intrinsic spin and the direction of the magnetic dipole moment are always parallel). Once aligned the magnetic dipole moments act together and form the magnetic field of the coil.
The main point is that a current from positrons as well as a stream of protons form a opposite magnetic field to this of the stream of accelerated electrons. Their intrinsic spins and magnetic dipole moments are antiparallel to this quantities of electrons and anti-protons.
