All Problems Electromagnetic Waves. Radiation
Problem 4.193
A plane electromagnetic wave \(\mathbf{E}=\mathbf{E}_ {m} \cos (\omega t-\mathbf{k r})\), where \(\mathbf{E}_ {m}=E_{m} \mathrm{e}_ {y}, \mathbf{k}=k \mathrm{e}_ {x}, \mathrm{e}_ {x}, \mathrm{e}_ {y}\) are the unit vectors of the \(x\) \(y\) axes, propagates in vacuum. Find the vector \(\mathrm{H}\) at the point with radius vector \(\mathbf{r}=x e_{x}\) 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 \(t_{0}=\) \(=33 \mathrm{~ns}\)
4.193. (a) \(\mathbf{H}=\mathbf{e}_{z} E_{m} \sqrt{\varepsilon_{0} / \mu_{0}} \cos k x=-0.30 \mathbf{e}_{z}\) (b) \(\mathbf{H}=\mathbf{e}_{z} E_{m} \sqrt{\varepsilon_{0} / \mu_{0}} \cos \left(c k t_{0}-k x\right)=0.18 \mathbf{e}_{z}\). Here \(\mathbf{e}_{z}\) is the unit vector of the \(z\) axis, \(H\) is expressed in \(\mathrm{A} / \mathrm{m}\)