Elementary experimental information about magnetostatic field production by turned‐on current sources suggests that such fields are nonpropagating superpositions of electromagnetic waves. It is shown that the local structure of these waves may be deduced from the Lorentz force law and the transformations of special relativity, without the intervention of Maxwell’s equations. The electromagnetic energy density formula is identified in the context of field production by a model ‘‘circuit’’ consisting of opposed parallel current sheets. Coulomb’s law of electrostatics is deduced by transforming the magnetostatic field of this circuit into the rest frames of the source particles.

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