An electromagnetic wave is represented by the electric field vecE =E0 hatn sin[ω t+(6y-8z)] . Taking unit vectors in x, y and z directions to be hat i , hatj , hatk , the direction of propogation hats , is :

Question

An electromagnetic wave is represented by the electric field vecE =E0 hatn sin[ω t+(6y-8z)] . Taking unit vectors in x, y and z directions to be hat i , hatj , hatk , the direction of propogation hats , is : (A)  hats = (4 hatj - 3 hatk/5) (B)  hats = (3 hatj - 4 hatk/5) (C)  hats = ( (-3 hatj + 4 hatk/5) ) (D)  hats = (-4 hatj + 3 hatk/5)

Tardigrade Admin · Accepted Answer

vecE = E0 hatn sin (ω t + (6y - 8z)) = E0 hatn sin (ω + veck . vecr) where vecr = x hati + y hatj + z hatk and veck . vecr = 6 y - 8z ⇒ veck = 6 hatj - 8 hath direction of propagation hats = - hatk = ( ( -3 hatj + 4 hatk/5) )

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

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

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

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

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

$E = E_{0} \overset{n}{^} sin (ω t + (6 y - 8 z))$
$= E_{0} \overset{n}{^} sin (ω + k . r)$
where $r = x \hat{i} + y \hat{j} + z \hat{k}$
and $k . r = 6 y - 8 z$
$\Rightarrow k = 6 \hat{j} - 8 \hat{h}$
direction of propagation
$\overset{s}{^} = - \hat{k}$
$= (\frac{- 3 j ^ + 4 k ^}{5})$

Q. An electromagnetic wave is represented by the electric field E=E0​n^sin[ωt+(6y−8z)] . Taking unit vectors in x,y and z directions to be i^,j^​,k^, the direction of propogation s^ , is :

s^=54j^​−3k^​

s^=53j^​−4k^​

s^=(5−3j^​+4k^​)

s^=5−4j^​+3k^​