Calculating Loss Tangent and Poynting Vector for Electromagnetic Waves

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In summary, we have a conversation about two different topics: (1) a source of unidirectional plane waves in a medium with moderate conductivity, and (2) a perfect planar mirror and its effects on electromagnetic waves. In the first topic, we are given complex electric field amplitudes and asked to calculate the loss tangent and the ratio of complex magnetic field amplitudes. In the second topic, we are given equations for phase velocity and group velocity, as well as information on circular polarization and the Poynting vector. The conversation ends with a request for help and an invitation to share any attempted solutions.
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unstoppable
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Hi can someone help me out with these questions? I would greatly appreciate it!

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=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. Homework 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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  • #2
Hi unstoppable! :smile:

(have a theta: θ and an omega: ω and an epsilon: ε :smile:)

Show us what you've tried, and where you're stuck, and then we'll know how to help. :wink:
 

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