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## gerryliyana Group Title Assume from electricity the following equations which are valid in free space. (They are called Maxwell equations) one year ago one year ago

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1. gerryliyana Group Title

$$\nabla . \bar E = 0$$ $$\nabla . \bar H = 0$$ $$\nabla \times \bar E=-\mu (\frac{ \delta \bar H }{ \delta t }$$) $$\nabla \times \bar E=-\epsilon (\frac{ \delta \bar E }{ \delta t }$$) 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 Group Title

have idea @CarlosGP ????

3. CarlosGP Group Title

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 Group Title

@CarlosGP and then what should i do ??

5. gerryliyana Group Title

Where are you getting these $\frac{ \delta^{2} E }{ \delta^{2}t } = - \omega ^{2} E_{s}$ ????

6. gerryliyana Group Title

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 Group Title

Hi @BAdhi

8. BAdhi Group Title

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 Group Title

cool @BAdhi ..., then.., what's the next? would you like to check my work above before you?

10. gerryliyana Group Title

hi @Jonask nice to meet you :)

11. Jonask Group Title

nice to meet you too are you taking electrıcty wıth edx

12. gerryliyana Group Title

no i'm not.., i'm taking 2.01x Elements of Structures

13. gerryliyana Group Title

@Jonask , would you like to check my work above??

14. Jonask Group Title

not famılıar wıth these sorry

15. perl Group Title

whats elements of structures?