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gerryliyana

  • 2 years ago

Assume from electricity the following equations which are valid in free space. (They are called Maxwell equations)

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  1. gerryliyana
    • 2 years ago
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    \(\nabla . \bar E = 0 \) \(\nabla . \bar H = 0 \) \(\nabla \times \bar E=-\mu (\frac{ \delta \bar H }{ \delta t }\)) \(\nabla \times \bar E=-\epsilon (\frac{ \delta \bar E }{ \delta t }\)) from them show that any component of \(\ \bar E\) or \(\ \bar H \) satisfies the wave equation with \(\ v = (\epsilon \mu )^{-1/2}\). Hint: use vector identity!

  2. gerryliyana
    • 2 years ago
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    have idea @CarlosGP ????

  3. CarlosGP
    • 2 years ago
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    Yes. I have. You should start by correcting the fourth equation. The right one is: \[\nabla \times H=\epsilon \frac{ \delta E }{ \delta t } \] How to obtain the wave equation from this particular case of Maxwell equations, can be found in any book of Electromagnetism

  4. gerryliyana
    • 2 years ago
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    @CarlosGP and then what should i do ??

  5. gerryliyana
    • 2 years ago
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    Where are you getting these \[\frac{ \delta^{2} E }{ \delta^{2}t } = - \omega ^{2} E_{s} \] ????

  6. gerryliyana
    • 2 years ago
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    then for Ey \[E_{ys} = E_{ys} (x) \rightarrow \frac{ \delta^{2}E_{ys} (x) }{ \delta z^{2} } =0 ; \frac{ \delta^{2}E_{ys}(x) }{ \delta y^{2} }=0 \] \[\frac{ \delta^{2}E_{ys} (x) }{ \delta x^{2} } + \left( \frac{ \omega }{ v } \right)^{2} E_{ys} = 0\] and for z \[E_{zs} = E_{zs} (x) \rightarrow \frac{ \delta^{2} E_{zs}(x) }{ \delta z^{2} }=0 ; \frac{ \delta^{2}E_{zs}(x) }{ \delta y^{2} }=0\] \[\frac{ \delta^{2} E_{zs} (x) }{ \delta x^{2} } + \left( \frac{ \omega }{ v } \right)^{2} E_{zs} =0\] correct me if i wrong.., :)

  7. gerryliyana
    • 2 years ago
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    Hi @BAdhi

  8. BAdhi
    • 2 years ago
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    we assume that E field is time harmonic, i.e. $$E=E_0e^{j\omega t}\implies \frac{d^2E}{dt^2}=-\omega^2E_0e^{j\omega t}=-\omega^2E$$

  9. gerryliyana
    • 2 years ago
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    cool @BAdhi ..., then.., what's the next? would you like to check my work above before you?

  10. gerryliyana
    • 2 years ago
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    hi @Jonask nice to meet you :)

  11. Jonask
    • 2 years ago
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    nice to meet you too are you taking electrıcty wıth edx

  12. gerryliyana
    • 2 years ago
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    no i'm not.., i'm taking 2.01x Elements of Structures

  13. gerryliyana
    • 2 years ago
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    @Jonask , would you like to check my work above??

  14. Jonask
    • 2 years ago
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    not famılıar wıth these sorry

  15. perl
    • 2 years ago
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    whats elements of structures?

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