Question 129: EM waves

Question

An electromagnetic wave is represented by the electric field $$\overrightarrow E  = {E_0}\widehat n\sin \left[ {\omega t + \left( {6y - 8z} \right)} \right]$$
. Taking unit
vectors in x, y and z directions to be $$\widehat i,\widehat j,\widehat k$$
, the direction of propagation $$\widehat s$$, is :

Accepted Answer

$$\overrightarrow E  = {E_0}\widehat n\sin \left( {\omega t + \left( {6y - 8z} \right)} \right)$$
$$ = {E_0}\widehat n\sin \left( {\omega t + \overrightarrow k .\overrightarrow r } \right)$$
where $$\overrightarrow r  = x\widehat i + y\widehat j + z\widehat k$$ and $$\overrightarrow k .\overrightarrow r  = 6y - 8z$$
$$ \Rightarrow \overrightarrow k  = 6\widehat j - 8\widehat k$$
direction of propagation
$$\widehat s =  - \widehat k = \left( {{{ - 3\widehat j + 4\widehat k} \over 5}} \right)$$

Answer

$$\widehat s = {{3\widehat i - 4\widehat j} \over 5}$$

Answer

$$\widehat s = {{ - 4\widehat k + 3\widehat j} \over 5}$$

Answer

$$\widehat s = \left( {{{ - 3\widehat j + 4\widehat k} \over 5}} \right)$$

Answer

$$\widehat s = {{4\widehat j - 3\widehat k} \over 5}$$

EM waves

An electromagnetic wave is represented by the electric field $\overrightarrow E = {E_0}\widehat n\sin \left[ {\omega t + \left( {6y - 8z} \right)} \right] . Taking unit vectors in x, y and z directions to be \widehat i,\widehat j,\widehat k , the direction of propagation \widehat s$, is :

Choose the correct answer: