Right-hand_rule

I believe he is saying there is nothing about the magnetic field that says "this is the direction" of the field any more than the positive charge is " positive". We just decided this charge is this one and the other charge is that one. I believe a professor once made the point that the right hand r ule could just as easily been the left hand rule as long as all the other c onventions it impacts were also changed.

Ok but that's obvious if that's all he meant.

Well, not all others, just an odd number of them. I always found the vector hand rules not very helpful because I always forgot which vector goes with which finger.

Same with using the 3 fingers right hand rule to tell if two parallel wires carrying a current are going to repel each other or attract each other by looking at the direction of Force. As long as the convention is the same for both wires, it works.

Not so. The direction of B is specified by Maxwell's equations, so once you decide which direction of current is positive, you've also decided the direction of B. There's only one arbitrary choice, not two.

The vector cross product obeys a right-hand thread rule--if you rotate vector A through an angle theta to make it parallel with vector B, then the polarity of their cross product is as if it were the point of a screw with a right-hand thread. (You pick the sense of rotation in which theta