qualitative proof of the transverse nature of em waves
Answers
In advanced 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
Answer:
DEaR go through the attachment
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