The electric field of an electromagnetic wave in free space is given by $\vec{E}=10 \cos \left(10^7 t+k…
The electric field of an electromagnetic wave in free space is given by
$\vec{E}=10 \cos \left(10^7 t+k x\right) \hat{j} V / m$, where $t$ and $x$ are in seconds and metres respectively. It can be inferred that
(1) The wavelength $\lambda$ is $188.4 \mathrm{~m}$.
(2) The wave number $k$ is $0.33 \mathrm{rad} / \mathrm{m}$.
(3) The wave amplitude is $10 \mathrm{~V} / \mathrm{m}$.
(4) The wave is propagating along.t $x$ direction
Which one of the following pairs of statements is correct?
(3) and (4)
(1) and (2)
(2) and (3)
(1) and (3)
Solution
The electric field of electromagnetic wave
$\begin{aligned}
& \overrightarrow{\mathrm{E}}=10 \cos \left(10^7 \mathrm{t} \pm \mathrm{kx}\right) \hat{\mathrm{j}} \\
& \text { Amplitude }=10 \mathrm{~V} / \mathrm{m} \\
& \because \quad \mathrm{c}=\frac{\omega}{\mathrm{k}} \\
& \therefore \quad 3 \times 10^8=\frac{10^7}{\mathrm{k}} \\
& \text { or } \quad k=\frac{1}{30} \\
& \text { or } \quad \frac{2 \pi}{\lambda}=\frac{1}{30} \\
& \text { or } \quad \lambda=188.4 \mathrm{~m} \\
&
\end{aligned}$
So, (1) and (3) option are correct.