What we know about physics can be summarized in very compact form. Classical electrodynamics is a subject that remains of immense practical importance as well as foundational for the modern field theories of particle physics and relativity. The equations that describe it can occupy less than a fourth of one of these lines of text. See, e.g., the tensor and differential form versions of Maxwell's equations in this Wikipedia article.
Chad Orzel recently wrote a post on teaching so-called Modern Physics, which is conveniently summarized as the physics discovered between 1899 and 1950. In particular he makes the case for teaching the history of the discoveries. His point is that you can learn a lot from understanding how the laws of physics were discovered and why we believe them - but read Chad's version, he's a good writer.
The alternative method, and it's also used a lot in physics, is to just write down the equations and then develop the mathematical techniques one can use to deduce their consequences. If one picks up a graduate level book in classical electrodynamics (e.g., Jackson's Classical Electrodynamics) that's mostly the approach you will get. In the US, anyway, physics students tend to get a three-layer approach to electricity and magnetism, starting with experimental results and formulation in calculus of integral equations in a General Physics course, with an intermediate layer from a book like Griffiths and Jackson as a sort of finale.
The historical approach can be instructive, but it can also be slow to recapitulate all the steps and there is a mountain of mathematical technique to learn.