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1. Why didn't we define the magnetic field to be in the directions of the force? This isn't really a technical question, I am just more curious about why it is this way. The way I was thinking of it, the math seems to get a little more complicated. The velocity would be perpendicular to the magnetic field if it were defined that way, but we can't really represent this with the cross product because the direction would be wrong. So is it just for lack of a better mathematical representation?

2. How does magnetism fit in with relativity? Not really advanced special relativity, but just the fact that all motion is relative. From my understanding of it, a magnetic field is caused by a moving source charge (or collection of charges), but a charge (not the source charge) only feels a force if it is moving. So, if we change our reference frame to make the source charge stationary, wouldn't the source charge only cause an electric field? There must be some flaw in my understanding of magnetism here because this would mean that a motionless charge can feel a magnetic force.