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(C) The electric field is $\vec{E} = -301.6 \sin (kz - \omega t) \hat{a}_{x} + 452.4 \sin (kz - \omega t) \hat{a}_{y}$.For an electromagnetic wave,the

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$-0.8 \sin (kz - \omega t) \hat{a}_{y} - 1.2 \sin (kz - \omega t) \hat{a}_{x}$

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(C) The electric field is $\vec{E} = -301.6 \sin (kz - \omega t) \hat{a}_{x} + 452.4 \sin (kz - \omega t) \hat{a}_{y}$.For an electromagnetic wave,the relationship between the amplitudes is $B_{0} = E_{0} / c$ and $H_{0} = B_{0} / \mu_{0} = E_{0} / (c \mu_{0})$.Given $c = 3 	imes 10^{8} 	ext{ m/s}$ and $\mu_{0} = 4\pi 	imes 10^{-7} 	ext{ T m/A}$,the impedance of free space is $Z_{0} = \mu_{0} c = 4\pi 	imes 10^{-7} 	imes 3 	imes 10^{8} \approx 377 	ext{ } \Omega$.The magnetic field components are $H_{x} = -E_{y} / Z_{0}$ and $H_{y} = E_{x} / Z_{0}$.Calculating the coefficients: $301.6 / 377 = 0.8$ and $452.4 / 377 = 1.2$.Using the direction property $\hat{k} = \hat{E} 	imes \hat{H}$,for $\vec{E} = E_{x} \hat{i} + E_{y} \hat{j}$,the magnetic field is $\vec{H} = \frac{1}{Z_{0}} (E_{y} \hat{i} - E_{x} \hat{j})$.Substituting the values: $\vec{H} = \frac{1}{377} [452.4 \sin (kz - \omega t) \hat{i} - (-301.6 \sin (kz - \omega t)) \hat{j}] = 1.2 \sin (kz - \omega t) \hat{i} + 0.8 \sin (kz - \omega t) \hat{j}$.Re-evaluating the vector directions based on the wave propagation in $+z$ direction: $\vec{H} = -0.8 \sin (kz - \omega t) \hat{a}_{y} - 1.2 \sin (kz - \omega t) \hat{a}_{x}$.

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