jfierro
- 20
- 1
Hi, I am not sure whether this falls into a math category or here, I hope you can help me.
I came across a problem in a book [bare with me, please] (Fundamentals of engineering electromagnetics by Cheng) and asked my electromagnetics profesor, but his response did not help me into getting to the result from the book, I later found that my profesor may have commited a mistake, this is the problem from the book:
6.20.- Given
in the air, determine
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \textbf{H}(x, z; t) \ and \ \beta
The thing is, my electromagnetics profesor insists in saying that for this problem:
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \beta = \omega\sqrt{\mu\epsilon} \approx 62.83
But I think this would apply only if it were only a function of z and not x for this particular wave. The method described in the book we are using consists on applying the following maxwell equations twice and then compare the resulting E field with the original E field so that we can obtain beta:
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \\ \nabla \times \textbf{E} = -j\omega \mu \textbf{H} \\ \nabla \times \textbf{H} = \textbf{J} + j\omega \epsilon \textbf{E}
Following this method I get:
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \beta^2 = \omega^2 \mu\epsilon} - 100\pi^2 \approx 54.41^2
Which is the result from the book.
My profesor goes as far as to say this method is invalid because is as though we were using a single equation to solve a 2 variable system...
Any ideas on how to refute him?
I came across a problem in a book [bare with me, please] (Fundamentals of engineering electromagnetics by Cheng) and asked my electromagnetics profesor, but his response did not help me into getting to the result from the book, I later found that my profesor may have commited a mistake, this is the problem from the book:
6.20.- Given
in the air, determine
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \textbf{H}(x, z; t) \ and \ \beta
The thing is, my electromagnetics profesor insists in saying that for this problem:
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \beta = \omega\sqrt{\mu\epsilon} \approx 62.83
But I think this would apply only if it were only a function of z and not x for this particular wave. The method described in the book we are using consists on applying the following maxwell equations twice and then compare the resulting E field with the original E field so that we can obtain beta:
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \\ \nabla \times \textbf{E} = -j\omega \mu \textbf{H} \\ \nabla \times \textbf{H} = \textbf{J} + j\omega \epsilon \textbf{E}
Following this method I get:
[PLAIN]http://latex.codecogs.com/gif.latex?0dpi[/URL] \beta^2 = \omega^2 \mu\epsilon} - 100\pi^2 \approx 54.41^2
Which is the result from the book.
My profesor goes as far as to say this method is invalid because is as though we were using a single equation to solve a 2 variable system...
Any ideas on how to refute him?
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