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The electric field of an EM wave in a dielectric medium is E = 30*(x_hat + y_hat)*sin[2*pi*(5*10¹⁴*t - (10⁷/3)*z)] V/m. Which of the following are correct? (c = 3*10⁸ m/s)

1. Bx = -2*10⁻⁷ * sin[2*pi*(5*10¹⁴*t - (10⁷/3)*z)] Wb/m²
2. By = 2*10⁻⁷ * sin[2*pi*(5*10¹⁴*t - (10⁷/3)*z)] Wb/m²
3. The wave is polarized in the xy-plane with polarization angle 45 deg with respect to the x-axis.
4. The refractive index of the medium is 2.

Correct answer: The refractive index of the medium is 2.

Solution

v = (5*10¹⁴)/(10⁷/3) = 1.5*10⁸ m/s. n = 3*10⁸/1.5*10⁸ = 2. Option D correct. E has equal x and y components (ratio 1:1), so polarization angle = 45 deg (not 30 deg as originally stated - checking corrected options). B = (k_hat x E)/v = (z_hat x 30*(x_hat+y_hat))*sin[...] / 1.5*10⁸. z x x = y, z x y = -x. So B = 30*(y_hat - x_hat)*sin[...]/(1.5*10⁸) = 2*10⁻⁷*(y_hat - x_hat)*sin[...]. Bx = -2*10⁻⁷ sin[...], By = +2*10⁻⁷ sin[...]. Options A, B, D all correct. Rephrased option C gives 45 deg (correct).

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