Is there a reason that magnetic field lines are drawn from north to south or is this a purely arbitrarily defined protocol (for convenience)? Essentially what I am asking is: without a reference magnet (like the earth) is there a way determining what pole of a magnet is north and which is south?
[Physics] the difference between north and south magnetically
electromagnetism
Best Answer
Lagerbaer's comment is correct: you can tell which way the magnetic field vectors point (i.e., which end of your bar magnet is "north") using a moving charge rather than a reference magnet.
But it's worth adding one more point: the original decision to draw magnetic field lines going away from "north" poles of magnets and towards "south" poles was an arbitrary one. We could have decided to draw all magnetic field lines the other way around, in which case the direction of the Lorentz force would be $-q({\bf v}\times{\bf B})$ instead of $q({\bf v}\times{\bf B})$. We'd either replace the right-hand rule with a left-hand rule, or more likely just reverse the order of ${\bf v}$ and ${\bf B}$ in the cross product, and keep using the same right-hand rule but with ${\bf v},{\bf B}$ interchanged.
Of course, we could also have decided to draw all electric fields the other way around too, by flipping the signs of all electric charges. Arguably some things would be simpler if the electron charge had originally been taken to be positive -- current would flow in metals in the same direction that the charges were moving, for instance -- but it's too late now.