Question

The electric field part of an electromagnetic wave in a medium is represented by: $E_{x}=0 $
$E_{y}=2.5 \frac{N}{C} \cos \left[\left(2 \pi \times 10^{6} \frac{ rad }{ m }\right) t-\left(\pi \times 10^{-2} \frac{ rad }{ s }\right) x\right]$
$E_{z}=0 $ The wave is :

• A. moving along $x$ direction with frequency $10^6\, Hz$ and wavelength $100\, m$
• B. moving along $x$ direction with frequency $10^6\, Hz$ and wavelength $200\, m$
• C. moving along $- x$ direction with frequency $10^6\, Hz$ and wavelength $200\, m$
• D. moving along $y$ direction with frequency $2\pi \times 10^{6}\,Hz$ and wavelength $200\, m$

Answer 1

Answer: (B)

$E_{y}=2.5 \frac{ N }{ C }\left[\left(2 \pi \times 10^{6} \frac{ rad }{ m }\right) t-\left(\pi \times 10^{-2} \frac{ rad }{ s }\right) x\right]$
$E_{z}=0$
The wave is moving in the positive direction of $x$.
This is the form $E_{y}=E_{0}(\omega t-k x)$
$\omega=2 \pi \times 10^{6} $
$2 \pi v=2 \pi \times 10^{6} $
$\Rightarrow v=10^{6} Hz $
$\frac{2 \pi}{\lambda}=k$
$ \Rightarrow \frac{2 \pi}{\lambda}=\pi \times 10^{-2} $
$\Rightarrow \lambda=\frac{2 \pi}{\pi \times 10^{-2}}$
$=2 \times 10^{2}=200\, m$