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In electromagnetic field, which one of the following does not satisfy the wave equation? 

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UPSC ESE (Prelims) Electronics and Telecommunication Engineering 19 Feb 2023 Official Paper
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  1. 25ei(ωt - 3z)
  2. sin (ω(27z + 15t))
  3. sin(x) cos(t) 
  4. cos(y2 + 5t) 

Answer (Detailed Solution Below)

Option 4 : cos(y2 + 5t) 
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Electromagnetic field:

Here, electromagnetic field compares electric and magnetic fields, essential for the behavior of charged particles and the transmission of electromagnetic waves.

Here, this cos(y2 +5t) option lacks spatial dependence on a coordinate like x, y, z. The absence of spatial dependence means it does not satisfy the wave equation. 

This involves a cosine function with respect to the spatial coordinates y2 and also includes a temporal component (y2).

Option 4 is correct.

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