An electromagnetic wave is represented by the electric filed E → = E 0 n ^ sin ⁡ ω t + 6 y - 8 z . Taking unit vectors in x , y and z directions to be i ^ , j ^ , k ^ , the directions of propogations

Question

An electromagnetic wave is represented by the electric filed E → = E 0 n ^ sin ⁡ ω t + 6 y - 8 z . Taking unit vectors in x , y and z directions to be i ^ , j ^ , k ^ , the directions of propogations s ^ , is:

TestHub · Accepted Answer

The standard equation of electromagnetic wave $\vec{E} = E_{0} \hat{n} \sin [ω t - k \hat{x}]$

here $\hat{x}$ represents the direction of propagation wave.

On comparing the given equation with the standard equation, the direction of propagation is along line $- 6 y + 8 z$ . Thus, unit vector along the direction of propagation is,
$\hat{s} = \frac{- 6 \hat{j} + 8 \hat{k}}{10} = - \frac{3}{5} \hat{j} + \frac{4}{5} \hat{k}$

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