Why do magnetic fields follow the right-hand rule instead of the left-hand rule?

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If a conductor connects your nose with the computerscreen with electricity going through it (allways in the same direction), the magnetic fieldlines will allways surround the conductor with one direction. Obviously nature prefers one direction more than the other.
Is there some very important consequenses of this asymmetri, and does it got a name?

I can more physics and english that it looks like in this post, so don't be shy with terms and other stuff.

Thank you.
 
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"Orientability"? Except... doesn't the Lorentz law cancel any consequence?
 
So you're wondering why magnetic fields orient themselves via the right-hand rule (as opposed to the left hand rule)?

The direction of the magnetic field is a mad-made convention, and not one enforced by nature (i.e. we could reverse all our conventions and still be consistent with nature). The effect of the field though (i.e. the resultant forces) retain the symmetry of the problem, the force in the case of a wire for example will always be directed either radially inward or outward.

Claude.