why does TEM waves have the same distribution of static fields in the transverse plane
The TEM fields of a signal in a coaxial cable at any instant are the same as static fields. There is a radial electric field due to the voltage difference between the conductors, and there is an azimuthal magnetic field between the two conductors due to the opposing electric currents in the two conductors. They obey Maxwell's equations. These signals travel at nearly the speed of light:
v = 1/sqrt(LC) where L and C are the inductance and capacitance per unit length. The ratio of the voltage and current is Z = sqrt(L/C).
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