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ExamsJEE MainPhysics

The electric field component of an electromagnetic wave in a medium is given by Eₓ = 0, E_y = 2.5 N/C cos[(2π × 10⁶ rad/m)x - (π × 10⁻² rad/s)t] ŷ, and E_z = 0. The wave is:

  1. propagating along the x-axis with frequency 10⁶ Hz and wavelength 100 m.
  2. propagating along the x-axis with frequency 10⁶ Hz and wavelength 200 m.
  3. propagating along the negative x-axis with frequency 10⁶ Hz and wavelength 200 m.
  4. propagating along the y-axis with frequency 2π × 10⁶ Hz and wavelength 200 m.

Correct answer: propagating along the x-axis with frequency 10⁶ Hz and wavelength 200 m.

Solution

The wave is described by the equation for the electric field, which indicates it propagates along the x-axis due to the x variable in the cosine function. The angular frequency is given as π × 10⁻² rad/s, leading to a frequency of 10⁶ Hz when converted, and the wave number is 2π × 10⁶ rad/m, which corresponds to a wavelength of 200 m.

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