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# Help needed in proving E cross H points in the same direction as K. watch

1. Hey all,

Having a bit of bother with this question. The first part asks you to find show the Eo is perpendicular to Ho, which I got no bother (Using a plane-wave ansatz) and ended up with Ho = K x Eo/(u*e) [u/e=permeability/permittivity]

The next part asks you to show that Eo x Ho points in the direction of K.
The second part i've always just assumed, and the notes literally just say (Please note also the KxE points in the direction of K). I know K points in the direction of propagation of the wave, and I also know that all three are perpendicular to each other.

Any help would be greatly appreciated, exam is tomorrow!

Question attached, cii.
2. So, I guess you should do something like this:

Because it is in the absence of matter, i.e. vacuum, you have and

As you have showed that , i.e. they are perpendicular, and gives and , which means the wave vector is perpendicular to the electric field and magnetic field. Thus, hence is in the same direction as
3. (Original post by agostino981)
So, I guess you should do something like this:

Because it is in the absence of matter, i.e. vacuum, you have and

As you have showed that , i.e. they are perpendicular, and gives and , which means the wave vector is perpendicular to the electric field and magnetic field. Thus, hence is in the same direction as
Ahhhh I see what you mean. Good idea, i'm sure that's what they are looking for.

Doing it mathematically I ended up with K.E = divE = 0, and obviously also K.H = divH = 0. Thus K is orthogonal to both E and H.

Thanks a lot for your help!

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Updated: January 6, 2013
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