Question

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

Answer 1

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

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!

Answer 2

have idea @CarlosGP ????

Answer 3

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

Answer 4

@CarlosGP and then what should i do ??

Answer 5

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

Answer 6

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.., :)

Answer 7

Hi @BAdhi

Answer 8

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

Answer 9

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

Answer 10

hi @Jonask nice to meet you :)

Answer 11

nice to meet you too are you taking electrıcty wıth edx

Answer 12

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

Answer 13

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

Answer 14

not famılıar wıth these sorry

Answer 15

whats elements of structures?