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

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    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 greatlyName:  hhhhh.png
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Size:  49.1 KB appreciated, exam is tomorrow!

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

    Because it is in the absence of matter, i.e. vacuum, you have \nabla \cdot E = 0 and \nabla \cdot H =0

    As you have showed that E\cdot H=0, i.e. they are perpendicular, \nabla \cdot E = 0 and \nabla \cdot H=0 gives  k\cdot E=0 and k\cdot H=0, which means the wave vector is perpendicular to the electric field and magnetic field. Thus, E\times H hence E_0 \times H_0 is in the same direction as k
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    (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 \nabla \cdot E = 0 and \nabla \cdot H =0

    As you have showed that E\cdot H=0, i.e. they are perpendicular, \nabla \cdot E = 0 and \nabla \cdot H=0 gives  k\cdot E=0 and k\cdot H=0, which means the wave vector is perpendicular to the electric field and magnetic field. Thus, E\times H hence E_0 \times H_0 is in the same direction as k
    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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