Conceptual Understanding in Introductory Physics XVIII

The Maxwell equations contain everything mentioned in an introductory calculus-based electromagnetic theory course, and then some. They contain detailed mathematical structure and deep insight into electromagnetic fields. They are a magnificent playground for learning the various theorems of vector calculus, and applying these theorems to the fields of particles naturally leads to things like divergence, […]

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Conceptual Understanding in Introductory Physics XVI

Superposition is a powerful principle in physics, especially in introductory electromagnetic theory. A charged particle’s electric field exists independently of the fields of any other particles. A thorough understanding of superposition can prevent the frequent misunderstanding that fields can somehow be “blocked,” which is subtly different from saying that the net field at a point […]

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Conceptual Understanding in Introductory Physics XV

Symmetry is part of the foundation¬†of contemporary physics, but it is seldom emphasized in introductory physics in proportion to its significance. There may be some value in discussing how symmetry applies to otherwise traditional introductory problems rather than just replicating numerical examples from a textbook (even a good textbook). These questions illustrate symmetry in electromagnetic […]

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Conceptual Understanding in Introductory Physics XIV

This post continues this series into second semester introductory calculus-based physics, usually electromagnetic theory. This question addresses basic DC circuits. In a traditional introductory e&m course, circuits are presented with so many idealizations that according to such treatments simple circuits shouldn’t work at all! Two of the most important idealizations are that potential differences along […]

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