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Finally wrapping up our dive into the different representations of Maxwell’s equations, we arrive at the vector potential forms. Unlike the other forms we’ve covered in past posts, there’s no perfect bottom-up derivation or stunning solution to a problem we can use to explain\u2014 nor how they rose from the backwaters of classical electromagnetism to take center stage in modern physics today.<\/p>\n\n\n\n
Let’s start at a place as good as any: simplifying Maxwell’s original equations. We’ll be focusing on the differential forms for this post, but for posterity here’s a brief recap of the whole set of equations and the physics they describe.<\/p>\n\n\n\n