Why does a magnetic field go anticlockwise of the direction of current?

Question

Why never clockwise? How does it 'know' to go anticlockwise?

Answer 1

The magnetic field is not a "vector", instead it is a bi-vector (skew-symmetrical tensor). In other words, it has a plane of action not direction. Here is a quote from Hermann Weyl "It may be justifiable on the grounds of economy of expression to replace skewsymmetrical tensors by vectors in ordinary vector analysis, but in some ways it hides the essential feature; it gives rise to the well-known “swimming rules” in electrodynamics, which in no wise signify that there is a unique direction of twist in the space in which electrodynamic events occur; they become necessary only because the magnetic intensity of field is regarded as a vector, whereas it is, in reality, a skewsymmetric tensor (like the so-called vectorial product of two vectors). If we had been given one more space-dimension, this could never have occurred"

and " ... when a magnetic field acts on a current element, whatever the inclination or orientation of the element at a given point, the force invariably acts in a locally fixed plane—Ampere’s directive plane—which is perpendicular to the conventional direction of the magnetic field", see for details John Roche "Axial vectors, skew-symmetric tensors and the nature of the magnetic field" Eur. J. Phys. 22 (2001) 193–203.

Answer 2

It is simply because of the convention we use for Field Lines. A different configuration would make it have a different direction.

Answer 3

Because somebody decided to have clocks running clockwise, and all clockmakers since then followed suite.

Answer 4

The direction of the magnetic field is defined in terms of its effect on a current (or moving charge). Specifically, the magnetic field points in a direction such that the force on a current will be in the $\vec{I}\times\vec{B}$ direction. (That's just a convention; there's no fundamental reason you must define the magnetic field direction that way.)

Meanwhile, parallel currents are observed to attract each other, so we know one current is producing a magnetic field and the other is experiencing it. If you work out which direction the magnetic field around the first current must point in order for $\vec{I}_2\times\vec{B}$ to point towards the first current, it's in the right-hand sense (or anticlockwise around the first current if the current is pointing towards you).