Suppose that the electric field of an electromagnetic wave in vacuum is $\mathbf{E}=\left(3.1 \mathrm{NC}^{-1} ight) \cos \left[1.8 \mathrm{rad} . \mathrm{m}^{-1} ight)$ $\left.y+\left(5.4 imes 10^6 \mathrm{rad} \mathrm{s}^{-1} ight) t ight] \hat{\mathbf{i}}$. What is the wavelength…

Question

Suppose that the electric field of an electromagnetic wave in vacuum is $\mathbf{E}=\left(3.1 \mathrm{NC}^{-1}ight) \cos \left[1.8 \mathrm{rad} . \mathrm{m}^{-1}ight)$ $\left.y+\left(5.4 	imes 10^6 \mathrm{rad} \mathrm{s}^{-1}ight) tight] \hat{\mathbf{i}}$. What is the wavelength $\lambda$ ?

Aicharya · Accepted Answer

Given that, equation of electric field of an electromagnetic wave in vacuum, $\mathbf{E}=\left(3.1 \mathrm{NC}^{-1}\right)$
$\cos \left[\left(1.8 \mathrm{rad} \mathrm{m}{ }^{-1}\right) y+\left(5.4 \times 10^6 \mathrm{rad} \mathrm{s}^{-1}\right) t\right] \hat{\mathbf{i}}$ We know that, general equation $\mathbf{E}=E_0 \cos [k y+w t] \hat{\mathbf{i}}$ Comparing Eqs. (i) and (ii), we get Propagation constant, $k=1.8 \mathrm{rad} / \mathrm{m}$ i.e., $\quad \frac{2 \pi}{\lambda}=1.8$ $\Rightarrow \quad \lambda=\frac{2 \pi}{1.8}=3.49 \mathrm{~m}$ Hence, wavelength of electromagnetic wave is $3.49 \mathrm{~m}$.

Suppose that the electric field of an electromagnetic wave in vacuum is $\mathbf{E}=\left(3.1…

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