Plane Wave Reflection from a Media Interface (Good Conductor)

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    Maxwell's equation
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The discussion focuses on the expressions for electric (E) and magnetic (H) fields in a good conductor and how to derive the Poynting vector from these equations. A discrepancy is noted between the derived results and those presented in a referenced textbook, particularly concerning the definition of the relationship between the two intrinsic impedances. Participants analyze the implications of this difference on the understanding of plane wave reflection at a media interface. The conversation emphasizes the importance of accurate definitions in electromagnetic theory. Clarification of these concepts is essential for resolving the inconsistencies observed.
baby_1
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Homework Statement
Obtaning the Poynting vector for the conductor
Relevant Equations
Maxwell Equation
Hi,
Below are the expressions for the electric (E) and magnetic (H) fields in a good conductor.
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Using those, the Poynting vector can be determined as follows.

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By applying the appropriate conversions and starting from these equations, we obtain:
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However, the result differs from the one in the book, where the relationship between the two intrinsic impedances is defined differently.

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Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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