# Time-varying uniform plane waves

• robert25pl
In summary, Daniel is discussing the expression for E and H as functions of time for a 30-MHz uniform plane wave propagating in a lossless medium with given parameters. They mention using Faraday's law in differential form to find the magnetic field and determining the electric field. They also discuss the propagation velocity and checking if E obeys all requirements before considering the problem solved.
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.

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

Daniel.

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:
$$E_{z,t} = 800 cos(60\pi 10^{6} t - 6.28*10^{-9} z + \varphi) \vec{i}$$

$$\varphi = -1.13$$

Last edited:
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.

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

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

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

Daniel.

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

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.

## 1. What are time-varying uniform plane waves?

Time-varying uniform plane waves, also known as electromagnetic waves, are a type of energy propagation that consists of oscillating electric and magnetic fields, perpendicular to each other and to the direction of propagation. They travel at the speed of light and are characterized by their frequency, wavelength, and amplitude.

## 2. How are time-varying uniform plane waves different from constant uniform plane waves?

Constant uniform plane waves have a fixed amplitude and frequency, whereas time-varying uniform plane waves have varying amplitudes and frequencies. This means that their electric and magnetic fields vary with time, creating a pattern of oscillation.

## 3. What is the significance of the time-varying aspect of these waves?

The time-varying nature of these waves allows for the transmission of information through modulating the amplitude, frequency, or phase of the wave. This makes them essential in various communication technologies, such as radio, television, and wireless networks.

## 4. How do time-varying uniform plane waves travel through different mediums?

Time-varying uniform plane waves can travel through a variety of mediums, including vacuum, air, and various materials. The speed of the wave may change depending on the properties of the medium, but the frequency and wavelength remain constant.

## 5. Can time-varying uniform plane waves be described by a mathematical formula?

Yes, time-varying uniform plane waves can be described by Maxwell's equations, which are a set of four partial differential equations that govern the behavior of electromagnetic waves. These equations relate the electric and magnetic fields to their sources and describe how they propagate through space and time.

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