For a wave characterized by Eox cos(w.t-k-z) Ez, t) = Eo. sin(w.t-koz) 0 V m plot E₂ (z, t) vs Ex (z, t) for one period at z=0. What type of polarization is this wave? W:=108 8 rad S Ex:=5 k:=0.5 rad Egy:=5

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For a wave characterized by:

\[
E(z, t) = 
\begin{bmatrix}
E_{0x} \cdot \cos(\omega \cdot t - k \cdot z) \\
E_{0y} \cdot \sin(\omega \cdot t - k \cdot z) \\
0
\end{bmatrix}
\cdot \frac{V}{m}
\]

- \(\omega = 10^8 \, \text{rad/s}\)
- \(k = 0.5 \, \text{rad/m}\)
- \(E_{0x} = 5\)
- \(E_{0y} = 5\)

Plot \(E_y(z, t)\) vs \(E_x(z, t)\) for one period at \(z = 0\). 

What type of polarization is this wave?

**Explanation:**

This representation describes the electric field vector \(\mathbf{E}(z, t)\) of an electromagnetic wave propagating along the z-axis. The components \(E_{0x}\) and \(E_{0y}\) determine the amplitude of the field in the x and y directions respectively. The wave frequency and wave number are given by \(\omega\) and \(k\).

**Task:**

Plot the trajectory of \(E_y\) against \(E_x\) to visualize the polarization of the wave, which should reveal whether the wave is linearly, circularly, or elliptically polarized.
Transcribed Image Text:For a wave characterized by: \[ E(z, t) = \begin{bmatrix} E_{0x} \cdot \cos(\omega \cdot t - k \cdot z) \\ E_{0y} \cdot \sin(\omega \cdot t - k \cdot z) \\ 0 \end{bmatrix} \cdot \frac{V}{m} \] - \(\omega = 10^8 \, \text{rad/s}\) - \(k = 0.5 \, \text{rad/m}\) - \(E_{0x} = 5\) - \(E_{0y} = 5\) Plot \(E_y(z, t)\) vs \(E_x(z, t)\) for one period at \(z = 0\). What type of polarization is this wave? **Explanation:** This representation describes the electric field vector \(\mathbf{E}(z, t)\) of an electromagnetic wave propagating along the z-axis. The components \(E_{0x}\) and \(E_{0y}\) determine the amplitude of the field in the x and y directions respectively. The wave frequency and wave number are given by \(\omega\) and \(k\). **Task:** Plot the trajectory of \(E_y\) against \(E_x\) to visualize the polarization of the wave, which should reveal whether the wave is linearly, circularly, or elliptically polarized.
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