An electromagnetic wave is represented by the electric field . Taking unit vectors in x, y and z directions to be , the direction of propagation , is :

Engineering

Physics

Electromagnetic Waves

Question

An electromagnetic wave is represented by the electric field $\vec{E} = E_{0} \hat{n} \sin [ωt + (6 y - 8 z)]$ . Taking unit vectors in x, y and z directions to be $\hat{i}, \hat{j}, \hat{k}$ , the direction of propagation , is :

$\hat{s} = \frac{3 \hat{j} - 4 \hat{k}}{5}$

$\hat{s} = (\frac{- 3 \hat{j} + 4 \hat{k}}{5})$

$\hat{s} = \frac{4 \hat{j} - 3 \hat{k}}{5}$

$\hat{s} = \frac{- 4 \hat{j} + 3 \hat{k}}{5}$

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$\vec{E} = E_{0} \hat{n} \sin (ωt + (6 y - 8 z) = E_{0} \hat{n} \sin (ωt + \vec{k} \cdot \vec{r}))$

$where \vec{r} = x \hat{i} + y \hat{j} + z \hat{k} and \vec{k} \cdot \vec{r} = 6 y - 8 z$

$\Rightarrow \vec{k} = 6 \hat{j} - 8 \hat{k}$

$Direction of propagation \hat{s} = - \hat{k}$

$= (\frac{- 3 \hat{j} + 4 \hat{k}}{5})$