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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?

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Yes, by looking what effect the magnetic field has on an electron – Lagerbaer May 18 '11 at 18:30
@Lagerbaer The right hand rule does make a convenient definition. – Dale May 18 '11 at 18:43
up vote 6 down vote accepted

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.

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+1 for mentioning the arbitrary naming of electric charges. – voithos May 18 '11 at 19:27
Were the two conventions (magnetic and electric field direction) decided independently? – Georg May 18 '11 at 20:02
I'm not an expert on the history, but they're certainly logically independent, and since both were decided before the unification of electricity and magnetism, I think they must have been historically independent decisions also. – Ted Bunn May 18 '11 at 20:12
In under the subtitle "Etymology" they mention some possible connection by Faraday. I'd like to read that paper from Faraday, but don't know how to get it. – Georg May 18 '11 at 20:43

The direction of the field lines is pure convention. Magnetic field lines are defined with respect to north magnetic "test charges" placed in the field (and how they move in the field). If they were defined with respect to test south magnetic test charges, the field lines would be reversed.

But as Lagerbaer points out, it is of course possible to distinguish between the two poles without using magnets - that is partly the point of "electromagnetism" :)

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