Question

The electric field part of an electromagnetic
wave in a medium is represented by $E_x=0;E_y=2.5\frac{N}{c}\cos \left[\right(2\pi \times {10}^6)t-(\pi \times {10}^{-2}\left)x\right];E_z=0;$
By the above characteristic, 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 $y$ direction with frequency ${10}^6$ $Hz$ and wavelength $100m$.
• D. moving along $y$ direction with frequency $2$$\pi \times$${10}^6$ $Hz$ and wavelength $200m$.

Answer 1

The correct option is A moving along $x$ direction with frequency ${10}^{6}Hz$ and wavelength $100m$.

$E_y=2.5\frac{N}{c}\left\{\right(2\pi \times {10}^6)t-(\pi \times {10}^6\left)x\right\};E_z=0$
The wave is moving in the positive direction of $x$. This is the form $E_y=E_0(wt-kx)\omega =2\pi \times {10}^{6}rad{s}^{-1}2\pi v=2\pi \times {10}^{6}rad{s}^{-1}\Rightarrow v={10}^6{s}^{-1}\frac{2\pi }{\lambda }=k\Rightarrow \frac{2\pi }{\lambda }=\pi \times {10}^{-2}\Rightarrow \lambda =\frac{2\pi }{\pi \times {10}^{-2}}=200m.$