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So im trying to work through the proof why why the direction of proporgation, the E field and B field are all orthogonal to one another.

What i have is...

[tex]E=E_{0}e^{i(k\ \bullet \ r-\omega t)}[/tex]

[tex]B=B_{0}e^{i(k\ \bullet \ r-\omega t)}[/tex]

[tex]\nabla \times E= -\frac{dB}{dt} \Rightarrow k \times E_{0}= \omega B_{0}[/tex]

[tex]\nabla \times B= \mu_{0}\epsilon_{0}\frac{dE}{dt} \Rightarrow k \times B_{0}= \mu_{0}\epsilon_{0}\omega E_{0}[/tex]

and i can see from this why k, B and E must be orthogonal. What im having difficulty with is how to get from the left to the right...

Any ideas?

What i have is...

[tex]E=E_{0}e^{i(k\ \bullet \ r-\omega t)}[/tex]

[tex]B=B_{0}e^{i(k\ \bullet \ r-\omega t)}[/tex]

[tex]\nabla \times E= -\frac{dB}{dt} \Rightarrow k \times E_{0}= \omega B_{0}[/tex]

[tex]\nabla \times B= \mu_{0}\epsilon_{0}\frac{dE}{dt} \Rightarrow k \times B_{0}= \mu_{0}\epsilon_{0}\omega E_{0}[/tex]

and i can see from this why k, B and E must be orthogonal. What im having difficulty with is how to get from the left to the right...

Any ideas?

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