Vlf waves in the ocean. the electric field component of a uniform plane vlf (very low frequency) electromagnetic field propagating vertically down in the z-direction in the ocean (σ = 4 s/m, ∈r = 81, , μr = 1) is approximately given by e (z, t) = x^e0e^-az cos(6π x10^3t - βz), where e0 is the electric field amplitude at z = 0^+ immediately below the air-ocean interface, at z = 0. note that the frequency of the wave is 3 khz.
(a) find the attenuation constant α and phase constant β.
(b) find the wavelength λ, phase velocity vp, skin depth δ, and intrinsic impedance ηc, and compare them to their values in air.
(c) write the instantaneous expression for the corresponding magnetic field h (z, t).