Time-varying uniform plane waves

[robert25pl]

I found the intrinsic impedance but I'm not sure which equation to choose?
Any suggestion? Thanks

Express both E and H as functions of time for a 30-Mhz uniform plane wave propagating in the positive z direction in a lossless medium having $$\varepsilon$$ = 20pR/m and $$\mu$$ = 5 uH/m. E has only an x component and it reaches a positive maximum amplitude of 800 v/m at z = 0.4m when t = 6ns.

 

[dextercioby]

Okay.Can u write the electric field...?You got all details.Polarization vector,magnitude,phase,frequency...

Daniel.

 

[robert25pl]

I got better textbook so I think I understand better now

$$E_{z,t} = E cos(\omega t - \beta z + \varphi) \vec{i}$$ for z>0

$$H_{z,t} = \frac{E}{\eta} cos(\omega t - \beta z + \varphi-\tau )\vec{j}$$ for z>0

Where $$\eta = \sqrt{\frac{\mu_{r}\mu_{o}}{\varepsilon_{r}\varepsilon_{o}}$$
but I'm not sure I should used $$\mu_{o}, and, \varepsilon_{o}$$
If yes then:
$$E_{z,t} = 800 cos(60\pi 10^{6} t - 6.28*10^{-9} z + \varphi) \vec{i}$$

$$\varphi = -1.13$$

 

[dextercioby]

Nope.U have to determine the electric field and then use Faraday's law in differential form (i hope you know how it looks like) to find the magnetic field.So worry only about the electric field & see whether you can add all pieces of the puzzle.

Write it

$$\vec{E}=E\sin\left (kz- \omega t+\varphi\right) \vec{i}$$

and then see what u're missing from the above expression.


Daniel.

 

[robert25pl]

I could not find that equation that you posted in my textbook so I got better book and I made changes above. Why do I need to use Faraday's law in differential form to get B and then H. A'm I wrong above "again"? Thanks

 

[dextercioby]

What's the propagation velocity...?And yes,

$$\nabla\times\vec{E}=-\mu \frac{\partial\vec{H}}{\partial t}$$

Daniel.

 

[robert25pl]

$$v_{p} = \frac{1}{\sqrt{\mu\varepsilon}} = \frac{\omega}{\beta}$$

 

[dextercioby]

It's okay,though that "beta" instead of "k" is rather awkward.Have you computed the B...?Did u check whether the E obeys all requirements...?

If so,then u're done with it.

Daniel.