A simple and common use of the Poynting vector is identification of direction of propagation of a wave or the direction of fields in space. Consider the magnetic field intensity

of a plane electromagnetic wave propagating in free space: \mathbf{H}=\hat{\mathbf{x}} H_{0} e^{j \beta y}+\hat{\mathbf{z}} H_{1} e^{j \beta y} \quad[\mathrm{~A} / \mathrm{m}] (a) Calculate the electric field intensity using the properties of the Poynting vector. (b) Show that the result in (a) is correct by substituting the magnetic field intensity into Maxwell's equations and evaluating the electric field intensity through Maxwell’s equations.

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