I remember I had somewhat of a difficult time trying to get the last two formulas in Maxwell's equations to make sense to me. Then one day I stumbled upon some physics textbook I found in the UHCL library that made something in my brain click. I reviewed the book on Amazon, but unfortunately I can't remember the name of the book at the moment.
I believe the book first mentioned how magnetic poles on a pair of magnets either attract or repel each other. But both do so more or less linearly. If you put an electric charge and a magnetic charge close to each other, the outcome is quite different. Instead of attracting or repelling each other linearly, the motion of one is almost perpendicular as the other approaches.
This clarified the whole circular motion in Maxwell's equations for me. Immediately the curl operation made sense, because before I was exposed to this idea it just seemed like an arbitrary operation in vector calculus.
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