Question

EM wavelength in water

1. At frequency w = 10 GHz, liquid water has a permittivity e = 1 i€2, With ei 80eo, 15€0, and a permeability u= Ho E2 (a) Starting from the Maxwell equations, show that the wave equation for EM waves in water, is given by VE(r, t) eHo2Er, t) (b) Show that the wave E(r, t) = żEg exp [i (kx - wt)] is a solution to the wave equation with k kR+ik, complex and w real. Derive two equations that kR and ki then obey (c) Derive an expression for the magnetic field component of the wave. Is it in phase with the electric field component? [Motivation required.] The solution to the two equations of (b) is 1 -E1 and ki w (d) The wave length in water of an EM wave with the given frequency is shorter than that of the same wave in vacuum Estimate by what factor it is shorter. [I need an estimate, not an exact calculation.

Answer 1

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