Hi there Jim,
As Nigel is implying i guess, when three things are orthogonal they are by definition mutually perpendicular, but the phrase you used although less common i think is still acceptable, especially if talking about two sets of separate orthogonal systems. In any case, it doesnt bother me for one
I am well aware of the charge and i better be aware of the makeup of the current (he he) that we always talk about here even if indirectly. But we dont want to let preconceived notions, even if true, dictate how we might want to think about an occurrence we see in real life, because we might let something go unnoticed, and after all most of the stuff we learn about we learn mostly because it is the simplest by product of previous thought, and is deemed a workable solution.
In this case, we learn about the effect of current flow and magnetic fields, and find a relationship such as curl(B)=u0*J and we use that with success to find out what will happen when we might have an occurrence where that is applicable, and so we walk away with a little satisfaction that we have found the answer to our dream of understanding physics. But have we really answered the question? There are a couple views on this, so lets look at it.
First, the mathematical description given by Maxwell was proven to be true for many cases, therefore it is the final answer and is perfect, and tells us EVERYTHING we need to know about that kind of occurrence. There is nothing wrong with this because the formula works, presumably every time. However, what can we say has really happened there?
Well, all we can say is that when we have a current flow in one direction and a magnetic field in another direction, the electrons in the current stream get deflected. We measure this and come up with a formula that describes it all and that seems to answer the question. However, that's just an after-the-fact explanation. We still dont know what the underlying reasons are. Let me give an example.
We stand in a position with a garden hose, while someone else throws a basketball past us. We start the water flow by squeezing the trigger, the water shoots at the basketball. The basketball gets deflected.
Now here is the thing...
Do we:
1. Make up a mathematical statement of what happened, like with the flow of the water and the speed of the basketball, and come up with a result every time and then call it quits, for example D=f(p,v), or
2. Do we try to look at every molecule of water and knowing the mass of each water particle and mass of the ball, and try to come up with a formula that way?
Well, in the case of curl(B)=u0*J we have done the first thing here. we came up with a formula for an overall observational fact and it works in all cases, so we call it quits. But if we take a closer look, we find that we really dont know what is really happening, we just know the effects of what has happened, logged them in a journal, and eek'd out a formula.
So although we think we are done mathematically, we still done know what exactly causes this reaction.
So when i said that the electron must be different than other objects, i was hinting that it is different in a way that may not be comprehensible down to the last final fact. Yes, we can say it has charge, and then that tells us something more, but then all we can say is that because charge is considered to be elementary to matter. So the implication here is that charge is not matter but is just part of matter, and that's really all we can say. To go back to the analogy with the water and ball, it's like saying the ball has mass, and not being able to say anything else about it. Of course with the electron we can say that it has a magnetic moment and that helps a little more, but the main idea is that the electron has such a different property than ordinary matter that it behaves so entirely different than other things.
Now let me describe another type of ball in the water and ball analogy. This ball, when the water hits it, does not fly off to the side opposite the water flow but always flies off in a direction that is downward. So see how different this new ball is
I guess this is an after the fact view too, where we see two things that behave differently under the same conditions and say, "It's different"
