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A plane electromagnetic wave \( \mathbf{E}=\mathbf{E}_{m} \cos (\omega t-\mathbf{k r}) \), where \( \mathbf{E}_{m}=E_{m} \mathbf{e}_{y} \), \( \mathbf{k}=k \mathbf{e}_{x}, \mathbf{e}_{x}, \mathbf{e}_{y} \) are the unit vectors of the \( x, y \) axes, propagates in vacuum. Find the vector \( H \) at the point with radius vector \( \mathbf{r}=x_{x} \) at the moment (a) \( t=0 \), (b) \( t=t_{0} \). Consider the case when \( E_{m}=160 \mathrm{~V} / \mathrm{m} \), \( k=0.51 \mathrm{~m}^{-1}, x=7.7 \mathrm{~m} \), and \( t_{0}=33 \mathrm{~ns} \)
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