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The electric field in a plane electromagnetic wave is given by
Eₓ = 60 cos (5x + 1.5 × 10⁹ 𝜃) V/m.
Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field):

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  1. Bᵧ = 2 × 10⁻⁷ cos (5x + 1.5 × 10⁹𝜃) T
  2. Bₓ = 2 × 10⁻⁷ cos (5x + 1.5 × 10⁹𝜃) T
  3. B𝓏 = 60cos (5x + 1.5 × 10⁹𝜃) T
  4. B𝓏 = 60sin (5x + 1.5 × 10⁹𝜃) T

Answer (Detailed Solution Below)

Option 1 : Bᵧ = 2 × 10⁻⁷ cos (5x + 1.5 × 10⁹𝜃) T
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Correct option is: (1) By = 2 × 10⁻⁷ cos(5x + 1.5 × 10⁹t) T
 
In electromagnetic waves, E and B are in the same phase and B0 = E0/c ; their planes are perpendicular to each other.
 
∴ By = (60 / c) cos(5x + 1.5 × 10⁹t) T
 
= (60 / 3 × 10⁸) cos(5x + 1.5 × 10⁹t) T
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