A) moving along y-direction with frequency \[2\pi \times {{10}^{6}}Hz\] and wavelength 200 m.
B) moving along\[x-\]direction with frequency \[{{10}^{6}}Hz\]and wavelength 100 m
C) moving along \[x-\]direction with frequency \[{{10}^{6}}Hz\]and wavelength 200 m
D) moving along\[x-\]direction with frequency \[{{10}^{6}}Hz\]and wavelength 200 m
Correct Answer: C
Solution :
The standard equation of electromagnetic wave \[{{E}_{y}}={{E}_{0}}\cos (\omega t-kx)\] The given equation \[{{E}_{v}}=2.5\frac{N}{C}\cos \left[ \left( 2\pi \times {{10}^{6}}\frac{rad}{m} \right)t-\left( \pi \times {{10}^{-2}}\frac{rad}{\sec } \right)x \right]\] Comparing with standard equation We get \[\omega =2\pi f=2\pi \times {{10}^{6}}\Rightarrow f={{10}^{6}}Hz\] Moreover, we know that \[\frac{2\pi }{\lambda }=k=\pi \times {{10}^{-2}}{{m}^{-1}}\Rightarrow \lambda =200\,m\] Hence, the wave is moving along positive \[x-\] direction with frequency 106 Hz and wavelength 200 m.
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