- #1
magnesium12
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Homework Statement
Write down the (real) electric and magnetic fields for a monochromatic plane wave of amplitude Eo, frequency w, and phase angle zero traveling in the direction from the origin to the point (1,1,1) with polarization parallel to the xz plane.
I understand how to write the equations, I just don't understand how to get the correct direction for the electric and magnetic fields.
Homework Equations
## E(z,t) = E_o\cos(\hat k \cdot \hat r - \omega t) \hat n ##
## B(z,t) = \frac{E_o}{c}\cos(\hat k \cdot \hat r - \omega t) ( \hat k x \hat n) ##
## k = -\frac{\omega}{c} ##
## \hat n \cdot \hat k = 0 ##
The Attempt at a Solution
This is what I did:
## \hat n = \hat x + \hat z ##
## \hat k = \frac{\omega}{c} (\hat x + \hat y + \hat z) ##
So I thought that was all I was supposed to do to find the direction, but the solutions manual says these are the actual directions of n and k:
## \hat n =\frac { \hat x - \hat z}{\sqrt{2}} ##
## \hat k = \frac{\omega}{c} \frac{(\hat x + \hat y + \hat z)}{\sqrt{3}} ##
So where did those factors of sqrt(2) and sqrt(3) come from?
I appreciate any help!