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)

moving along $x$ direction with frequency $10^6\, Hz$ and wavelength $200\, m$

Answer 2

The correct option is(B): moving along $x$ direction with frequency $10^6\, Hz$ and wavelength $200\, m$

As the coefficient of $x$ is negative, it is moving along +ve x-axis and equating the equation
$E _{ y }=2.5 \cos \left[\left(2 \pi \times 10^{6}\right) t -\left(\pi \times 10^{-2}\right) x \right]$
with $y = A \cos (\omega t - kx )$
$\omega =2 \pi \times 106$
$\Rightarrow f =\frac{\omega}{2 \pi}=10^{6}\, Hz$
$k =\pi \times 10^{-2}$
$\Rightarrow \lambda =\frac{2 \pi}{ k }$
$=\frac{2 \pi}{\pi \times 10^{-2}}=200\, m$