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1) A source of unidirection plane waves operates within a medium with moderate conductivity sigma. Suppose we measure the complex electric field amplitudes at the source and at some distance z and find that E(z)/E(0)-0.3-j0.4.

(a) Calculate the loss tangent sigma/(omega*epsilon) of the medium. (Give a numerical value)

(b) What is the ratio of complex magnetic field amplitudes H(z)/H(0) for the same z?

2) A perfect planar mirror in the xy-plane has normally incident and reflected electromagnetic plane waves in the vacuum region z<0 in front of it, at frequency omega. The magnetic field at the mirror surface is circularly polarized=H(x + jy)

(x and y are the unit vectors along x and y).

(a) Find the complex electric field amplitude E(z) in the space z<0.

(b) Find the complex Poynting vector(give magnitude and direction) in the space z<0.

2. Relevant equations

equation for phase velocity: Vp=Vp(omega)=omega/k= c*omega/squarerootof(omega^2-omega^2) Note: The second omega^2 is the cuttoff frequency

equation for group velocity: Vg=Vg(omega)=c*squarerootof(omega^2-omega^2)/(omega)

Note: The second omega^2 is the cuttoff frequency.

c=the speed of light 3 X 10^8 m/s

Circular Polarization: E(0)=Eox=1/2Eo(x+jy) +1/2Eo=(x-jy)

Note: j=the imaginary complex number

E(z)=1/2*Eo(x+jy)*e^-j(ko+K)z+1/2*Eo(x-jy)*e^-j(ko-K)z

Poynting Vector: The Vector E X H is the Poynting Vector. It gives the power per unit area that flows at a point;

Loss Tangent:Theta/(omega*epsilon)

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