# 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?

• Can't you decide on a default normal vector direction (usually outwards pointing (some kind of volume element being positive I think))? More often than not things like this are implicitly assumed and gives headache... – Emil Apr 11 '16 at 6:05