5.  A wave radiated by a source in air is incident upon a soil surface, whereupon a part of the wave is transmitted into the soil medium.  If the wavelength of the wave is 30 cm in air and 15 cm in the soil medium, what is the soil's relative permittivity?   Assume the soil to be a very low-loss medium.(α = 0.5σ sqrt(μ/ε) for low-loss mediums )
 

8. For a wave characterized by the electric field
                E(z,t)= x E_x cos(ωt -kz) +y E_y cos (ωt-kz +δ)
identify the polarization state, determine the polarization angles of each case:
a) E_x = 3 V/m , E_y = 4V/m and δ = 0^o
b) E_x = 3 V/m , E_y = 4V/m and δ = 180^o
c) E_x = 3 V/m , E_y = 3V/m and δ = 45^o
d) E_x = 3 V/m , E_y = 4V/m and δ = -135^o
 

17. Generate a plot for the skin depth δ_s versus frequency for seawater for the range from 1kHz to 10GHz (use log-log scales) .   The constitutive parameters of seawater can be taken as : relative permeability = 1 , relative permitivity = 80 and conductivity = 4S/m for that frequency range.
 
 

21.  The electric field of a plane wave propagating in a nonmagnetic medium is given by
             E(z,t)= z 25 e^-30x cos(2πx10⁹t -40x)

Obtain the corresponding expression for H.

30. At microwave frequencies, the power density considered safe for human exposure is 1 (mW/cm²).  A radar radiates a wave with an electric field amplitude E that decays with distance as  E(R) = (3,000/ R) [V/m], where R is the distance in meters.  What is the radius of the unsafe region?