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The electric field part of an electromagnetic wave in a medium is represented by E_x = 0; E_y = 2.5 \text{ N/C} \cos[(2\pi \times 10^6)t - (\pi \times 10^{-2})x]; E_z = 0. The wave is:

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 800 m

Step-by-Step Solution

  1. Wave Equation Analysis: The given electric field equation is of the form Ey=E0cos⁡(ωt−kx)E_y = E_0 \cos(\omega t - kx).
  • The term (ωt−kx)(\omega t - kx) indicates the wave is propagating in the positive x-direction.
  • The electric field oscillates in the y-direction (EyE_y component).
  1. Frequency Calculation: The angular frequency ω\omega is the coefficient of tt. ω=2πf=2π×106 rad/s\omega = 2\pi f = 2\pi \times 10^6 \text{ rad/s} f=106 Hzf = 10^6 \text{ Hz}
  2. Wavelength Calculation: The propagation constant (or angular wavenumber) kk is the coefficient of xx. k=2πλ=π×10−2 rad/mk = \frac{2\pi}{\lambda} = \pi \times 10^{-2} \text{ rad/m} λ=2ππ×10−2=210−2=200 m\lambda = \frac{2\pi}{\pi \times 10^{-2}} = \frac{2}{10^{-2}} = 200 \text{ m}
  3. Conclusion: The wave moves along the x-direction with a frequency of 106 Hz10^6 \text{ Hz} and a wavelength of 200 m200 \text{ m} .
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