The electric field part of an electromagnetic wave in a medium is represented by E_x = 0; E_y = 2.5 ext{ N/C

Question

The electric field part of an electromagnetic wave in a medium is represented by E_x = 0; E_y = 2.5 	ext{ N/C} \cos[(2\pi 	imes 10^6)t - (\pi 	imes 10^{-2})x]; E_z = 0. The wave is:

Accepted Answer

1. **Wave Equation Analysis:** The given electric field equation is of the form $E_y = E_0 \cos(\omega t - kx)$. 
   - The term $(\omega t - kx)$ indicates the wave is propagating in the positive **x-direction**.
   - The electric field oscillates in the y-direction ($E_y$ component).
2. **Frequency Calculation:** The angular frequency $\omega$ is the coefficient of $t$. 
   $$ \omega = 2\pi f = 2\pi 	imes 10^6 	ext{ rad/s} $$
   $$ f = 10^6 	ext{ Hz} $$
3. **Wavelength Calculation:** The propagation constant (or angular wavenumber) $k$ is the coefficient of $x$. 
   $$ k = \frac{2\pi}{\lambda} = \pi 	imes 10^{-2} 	ext{ rad/m} $$
   $$ \lambda = \frac{2\pi}{\pi 	imes 10^{-2}} = \frac{2}{10^{-2}} = 200 	ext{ m} $$ 
4. **Conclusion:** The wave moves along the x-direction with a frequency of $10^6 	ext{ Hz}$ and a wavelength of $200 	ext{ m}$ .

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