## gerryliyana 2 years ago Assume from electricity the following equations which are valid in free space. (They are called Maxwell equations)

1. gerryliyana

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

have idea @CarlosGP ????

3. CarlosGP

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

@CarlosGP and then what should i do ??

5. gerryliyana

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

6. gerryliyana

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

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

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

10. gerryliyana

hi @Jonask nice to meet you :)

nice to meet you too are you taking electrıcty wıth edx

12. gerryliyana

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

13. gerryliyana

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

not famılıar wıth these sorry

15. perl

whats elements of structures?