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The magnetic field of a plane electromagnetic wave in vacuum is given by: B = 2 10⁻⁸ (0.5 10^3 x + 1.5 10¹¹ t) j T Which of the following represents the corresponding vector equation for the electric field?

Options

  1. A6 (0.5 10^3 x + 1.5 10¹¹ t) (- k ) V/m
  2. B6 (0.5 10^3 x + 1.5 10¹¹ t) k V/m
  3. C6 (0.5 10^3 x + 1.5 10¹¹ t) i V/m
  4. D2 10⁻⁸ (0.5 10^3 x + 1.5 10¹¹ t) k V/m

Correct answer

B. 6 (0.5 10^3 x + 1.5 10¹¹ t) k V/m

Step-by-step solution

The phase of the wave is (kx + t) . Since both the x term and the t term have the same positive sign, the wave is propagating in the negative x -direction ( - i ). The direction of propagation is given by the cross product E B . We know the magnetic field B oscillates along the + j direction. Let the direction of the electric field be n . n j = - i Since k j = - i , the electric field must oscillate along the + k direction. The amplitude of the electric field E₀ is related to the magnetic field amplitude B₀ by: E₀

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