Question

The electric field part of an electromagnetic wave in a medium is represented by: $E_x=0$
$E_y=2.5\frac{N}{C}\cos \left[\left(2π×10^6\frac{rad}{m}\right)t−\left(π×10^{−2}\frac{rad}{s}\right)x\right]$
$E_z=0$ The wave is :

• A. moving along $x$ direction with frequency $10^{6}Hz$ and wavelength $100m$
• B. moving along $x$ direction with frequency $10^{6}Hz$ and wavelength $200m$
• C. moving along $−x$ direction with frequency $10^{6}Hz$ and wavelength $200m$
• D. moving along $y$ direction with frequency $2π×10^{6}Hz$ and wavelength $200m$

Answer 1

Answer: (B)

$E_y=2.5\frac{N}{C}\left[\left(2π×10^6\frac{rad}{m}\right)t−\left(π×10^{−2}\frac{rad}{s}\right)x\right]$
$E_z=0$
The wave is moving in the positive direction of $x$.
This is the form $E_y=E_0(ωt−kx)$
$ω=2π×10^6$
$2πv=2π×10^6$
$⇒v=10^{6}Hz$
$\frac{2π}{λ}=k$
$⇒\frac{2π}{λ}=π×10^{−2}$
$⇒λ=\frac{2π}{π×10^{−2}}$
$=2×10^2=200m$