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The electric field of a plane electromagnetic wave propagating in a transparent non-magnetic medium is given by E = 40 (1.2 10^8 t - 0.6 z) i V/m . The corresponding magnetic field equation will be:

Options

  1. A2 10⁻⁷ (1.2 10^8 t - 0.6 z) j T
  2. B1.33 10⁻⁷ (1.2 10^8 t - 0.6 z) j T
  3. C-2 10⁻⁷ (1.2 10^8 t - 0.6 z) j T
  4. D8 10^9 (1.2 10^8 t - 0.6 z) j T

Correct answer

A. 2 10⁻⁷ (1.2 10^8 t - 0.6 z) j T

Step-by-step solution

Given the electric field equation: E = 40 (1.2 10^8 t - 0.6 z) i V/m Comparing with the standard equation E = E₀ ( t - kz) i , we get: E₀ = 40 V/m = 1.2 10^8 rad/s k = 0.6 rad/m The speed of the wave in the medium is: v = k = 1.2 10^8 0.6 = 2 10^8 m/s The amplitude of the magnetic field is: B₀ = E₀ v = 40 2 10^8 = 2 10⁻⁷ T The wave propagates in the +z direction (since the phase is t - kz ), so v = k . The direction of the magnetic field is given by E B = v . i B = k B = j Therefore, the magnetic field equation is:

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