magnetic field directionality, mathematic rigmarole?

Phyzwizz

The force as a result of a moving charged particle through a magnetic field is perpendicular to the field apparently. Why should the magnetic field be perpendicular to the force created as a result. F.b=q(vXB) is the mathematical notation for this which accurately describes the world. But I cannot imagine why it would be impossible for math to describe the magnetic force instead in terms of a magnetic field that is parallel with it. So is the directionality of the magnetic field, simply just assigned by definition, or does it have some basis in reality that can actually be proven by experiment?

jtbell

Both the magnitude and direction of the magnetic force on a particle moving through a particular point in space (with a given surrounding arrangement of currents and/or moving charges) depend on the particle's speed and direction of motion. Two particles going through the same point with the same speed but in different directions, experience magnetic forces that (in general) have different magnitudes and directions. Therefore one cannot define a unique magnetic field at that point that has the same direction as the magnetic force.