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  • The electric field part of an electromagnetic wave in a medium is represented by <img alt="\mathrm{E_x=0,E_y=2.5 \frac{\mathrm{N}}{\mathrm{C}} \cos \left[\left(2^{\pi \times 10^6 \frac{\mathrm{rad}

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

Option: 1

moving along x direction with frequency 10^{6}\; \text{Hz} and
wavelength 100 m


Option: 2

moving along x direction with frequency 10^{6}\; \text{Hz} and
wavelength 200 m


Option: 3

moving along y direction with frequency  10^{6}\; \text{Hz} and
wavelength 200 m


Option: 4

moving along y direction with frequency 2 \pi \times 10^6 Hz and
wavelength 200 m


Answers (1)

\begin{aligned} & \mathrm{E}_{\mathrm{y}}=2.5 \frac{\mathrm{N}}{\mathrm{C}} \times \cos { }^{\lceil}\left[\left(2 \pi \times 10^{\circ} \frac{\mathrm{rad}}{\mathrm{m}}\right) \mathrm{t}-\left(\pi \times 10^{-2} \frac{\mathrm{rad}}{\mathrm{s}}\right) \mathrm{x}\right\rfloor \\ \\& \mathrm{E}_{\mathrm{z}}=0, \mathrm{E}_{\mathrm{x}}=0 \end{aligned}

The wave is moving in the positive direction of x.

This is in the form


 \\\mathrm{E}_{\mathrm{y}}=\mathrm{E} \cos (\mathrm{\omega t}-\mathrm{kx} )\\ \\\omega=2 \pi \times 10^6

\begin{aligned} & 2 \pi \mathrm{v}=2 \pi \times 10^6 \Rightarrow \mathrm{v}=10^6 \mathrm{~Hz} \\ \\& \frac{2 \pi}{\lambda}=\mathrm{k} \Rightarrow \frac{2 \pi}{\lambda} \quad \text { or } \lambda=200 \mathrm{~m} \end{aligned}

Posted by

Sumit Saini

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