# Determining Propagation vector from E(x,y,t)

1. Feb 12, 2014

### priceless

1. The problem statement, all variables and given/known data

E(x,y,t)=(2i/sqrt(5)) + (j/sqrt(5)) Eo cos( 2pi(1/lamda)[2x/sqrt(5) - y/sqrt(5)]-[ft] )

2. Relevant equations
I Know k =2pi/lamda for 1D wave
I know K vetor=k dot r
I know K vector shows the direction of propogation, and must be perpendicular to E and B.

3. The attempt at a solution
Got 1/3 points on this part of my exam.
Kvector=2pi (1/lamda) [2/sqrt(5) - 1/sqrt(5)] * (2i/sqrt(5)) + (j/sqrt(5))
I know I have to check for normalizaton, and it is normalized.

Obviously this is wrong. I'm not sure how to define k for a multi dimensional wave, and my textbook does not show any example problems for 3 dimensional waves., or shows solutions for any multidimensional waves that involve K.

Is the answer simply the resultant vector of kx and ky?
sqrt( (2/sqrt(5))^2 + (1/sqrt(5))^2)) which just equals sqrt(1)=1.

Edit: Referred back to Griffiths electrodynamics, and think I Figured it out.

K vector = K * r = (2pi/lamda) ( 2x^ / sqrt(5) - 1y^ / sqrt(5))
where x^ and y^ indicate the unit vectors xhat and yhat, not x to a power of ____.

Last edited: Feb 12, 2014
2. Feb 13, 2014

### maajdl

What is your question?
I don't see what the problem statement is.
Also what are the meaning of those i and j, are those things quaternions?
What is the meaning of [ft]?
Four us and for yourself, take a little bit more time to explain your question properly.

3. Feb 13, 2014

### priceless

Apologies, it was determine the propagation vector from this equation of a plane-polarized wave.

4. Feb 14, 2014

### BvU

Within the cosine, you see something that depends on x,y and something that depends on t.
Propagation has something to do with following time development of points (lines, planes) with constant E through time. $cos(\vec k \cdot \vec r - \omega t)$ I seem to remember.

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