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If let say i have an EMW given by- (Note the difference between $k$ and K)

B(x,y,z)=$B_0sin[(x+y)\frac{K}{√2}+wt]\hat k$

i got confused in 2 different outcomes when i wanted to find out the direction of propogation of the wave.

Case 1 -Since direction of propogation always points towards the wave vector K its should be $\frac{\hat i}{√2}+\frac{\hat j}{√2}$

Case 2 - Comparing the B(x,y,z) equation with the general equation for emw we know if coefficients of Kr and wt are same then wave propogates in negative r direction, here i got confused and dont know how to progress and find direction of r.

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    $\begingroup$ If you look at the derivation why a wave would propagate along the direction of the wave vector ${\bf k}$ you might see how this works out for this situation. $\endgroup$
    – Jos Bergervoet
    Commented Feb 26 at 17:37
  • $\begingroup$ I know K is defined as K= w/v where v is velocity of wave thus direction of wave velocity is direction of K. But i am confused about 'r' how am i supposed to find direction of r in this situation $\endgroup$
    – SHINU_MADE
    Commented Feb 26 at 17:47
  • $\begingroup$ Maybe look at this earlier question: physics.stackexchange.com/questions/376359/… $\endgroup$
    – Jos Bergervoet
    Commented Feb 26 at 17:52
  • $\begingroup$ The moderations want you to reformulate the question. Maybe you give some background of where you got the equation from. $\endgroup$
    – mond
    Commented Feb 26 at 19:04

1 Answer 1

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I assume K is a scalar value. The wave that is described by the above formular:

Describes a $\vec{B}$ filed that is always oriented in the $\vec{k}$ direction.

The wave propagation can only be in along $\vec{e_x}+\vec{e_y}$ direction. With a postive K it would be in the $-(\vec{e_x}+\vec{e_y}) $ direction with a wavelength of $\lambda=\frac{2\pi}{K}$.

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  • $\begingroup$ Well yes. But the field described by the equation describes a different field. The equations lets you calculate the field in every place in space and on each time. A field like this might be an approximation of a field in a limited place. E.g. Near some antenna. $\endgroup$
    – mond
    Commented Feb 26 at 18:55
  • $\begingroup$ If $\hat{k}$ is an arbitrary vector then that could still be be perpendicular to the direction of propagation. Since the original posting used $\hat{i}$ synonymus for $\vec{x}$ then k would mean z direction an be perpendicular... $\endgroup$
    – mond
    Commented Feb 26 at 20:44
  • $\begingroup$ Whoops, my mistake. It is transverse. I’ll delete my comments. And I’ve upvoted your answer. $\endgroup$
    – Ghoster
    Commented Feb 26 at 21:03
  • $\begingroup$ @mond i am not familiar with variable 'e' that you used in answer. What does it mean? $\endgroup$
    – SHINU_MADE
    Commented Feb 27 at 3:56
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    $\begingroup$ $\vec{e_x}$ would be the unit vector in the x direction. I think you used $\hat{i}$ instead. It is a matter of different tastes. I switched to using these more explicit form as in your original posting there is some ambiguity about all that. And then we electrical engineer have the symbol i reserved for the current (even to the point where we write the complex unit as j instead). $\endgroup$
    – mond
    Commented Feb 27 at 7:36

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