All Problems

Electromagnetic Waves. Radiation

Problem 4.192

A plane electromagnetic wave \(\mathbf{E}=\mathbf{E}_ {m} \cos (\omega t-\mathbf{k} \mathbf{r})\) propagates in vacuum. Assuming the vectors \(\mathrm{E}_ {m}\) and \(\mathbf{k}\) to be known, find the vector \(\mathrm{H}\) as a function of time \(t\) at the point with radius vector \(r=0\)

Reveal Answer
H=1kε0/μ0[kEm]cos⁡(ckt), where c is the velocity of the wave in vacuum\mathbf{H}=\frac{1}{k} \sqrt{\varepsilon_{0} / \mu_{0}}\left[\mathbf{k} \mathbf{E}_{m}\right] \cos (c k t), \text { where } c \text { is the velocity of the wave in vacuum}
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