I think what you are missing is that 3-D Cartesian coordinate systems themselves are either right-handed or left-handed. If the coordinates are of the form <x,y,z>, the to be right-handed it must be true that:Hi,
Yes thanks, that helps to clarify the right hand rule problem, which i am now going to call Problem #1. That works with the original wire and field i posted in the first post (wire along x, conventional current left to right along x, B field into the page).
Problem #2 comes in when we try to do the cross product. As i was saying before, the cross of two vectors U and V where they are:
U=[1,0,0] (wire length with conventional current flow)
V=[0,0,1] (mag field B)
and the cross product of U and V:
U x V = [0,-1,0]
shows a force oriented DOWN not UP as the right hand rule shows.
<1,0,0> x <0,1,0> = <0,0,1>
Your U vector is in the positive X direction, which you have defined as being left to right in the plane of the page. Your V vector is in the positive Z direction, which you have defined as being downward into the page. In order for this to be a right-handed coordinate system, your positive Y direction MUST go downward in the plane of the page. Thus, the vector [0,-1,0] is pointing upward in the plane of the page.