nced courses the transversality of electromagnetic waves is easily shown [10] from the Maxwell EQUATIONS and the wave equation for the vector potential Aµ in the Lorenz gauge, and the skew symmetry of the Maxwell–Faraday tensor Fµν := ∂µAν − ∂νAµ. Consider, say, a vector potential Aµ = A cos(kz − ωt) δ x µ. The only nonvanishing independent components of Fµν are Ftx = Ex and Fxz = By, and Ex = (ω/k)By. These E and B fields manifestly SATISFY the aforementioned properties, although the formality of the DEMONSTRATION —in addition to being inappropriate for the introductory course— is devoid of physical insight. (One may of course try to impose longitudinality: take Aµ = A cos(kz − ωt) δ z µ. One then finds that Ftz is non-zero, and one might be tempted to identify it with Ez. However, the postulated vector potential is not a solution for the Maxwell equations in the Lorenz gauge, as can be readily verified.) One can also SHOW the transversality without INVOKING tensor analysis, using only vector analysis methods