The electric field of an electromagnetic wave | vedclass

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(D) Given equation: $\vec E = 10 \cos (10^7 t + kx) \hat j \, V/m$.Comparing with the standard wave equation $\vec E = E_0 \cos (\omega t + kx) \hat j

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$(1)$ and $(3)$

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(D) Given equation: $\vec E = 10 \cos (10^7 t + kx) \hat j \, V/m$.Comparing with the standard wave equation $\vec E = E_0 \cos (\omega t + kx) \hat j$,we get:Amplitude $E_0 = 10 \, V/m$ (Statement $(3)$ is correct).Angular frequency $\omega = 10^7 \, rad/s$.Since the phase is $(\omega t + kx)$,the wave propagates in the $-x$ direction (Statement $(4)$ is incorrect).For electromagnetic waves in free space,$c = \frac{\omega}{k} = 3 	imes 10^8 \, m/s$.Thus,$k = \frac{\omega}{c} = \frac{10^7}{3 	imes 10^8} = 0.033 \, rad/m$ (Statement $(2)$ is incorrect).Wavelength $\lambda = \frac{2\pi}{k} = \frac{2 	imes 3.1416}{0.033} \approx 188.4 \, m$ (Statement $(1)$ is correct).Therefore,statements $(1)$ and $(3)$ are correct.

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