- #1

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kcos(kz - wt) = 0 which means that k = 0. This surely doesn't make sense?

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- #1

- 801

- 70

kcos(kz - wt) = 0 which means that k = 0. This surely doesn't make sense?

- #2

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- 0

Well, mathematically,

[tex] \bigtriangledown \cdot E_0 \cos(kz - wt) = E_0 \sin(kz - wt) = 0 [/tex]

[tex] \Longrightarrow k = 0[/tex] or [tex]sin(kz - wt) = 0[/tex] [tex]\forall{ z, t }[/tex]

EDIT: But yes, addressed below is the conceptual issue here...

[tex] \bigtriangledown \cdot E_0 \cos(kz - wt) = E_0 \sin(kz - wt) = 0 [/tex]

[tex] \Longrightarrow k = 0[/tex] or [tex]sin(kz - wt) = 0[/tex] [tex]\forall{ z, t }[/tex]

EDIT: But yes, addressed below is the conceptual issue here...

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- #3

nicksauce

Science Advisor

Homework Helper

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Consider a plane wave

[tex]\vec{E} = \vec{E_0}cos(\vec{k}\cdot\vec{r} - \omega t})[/tex]

Then,

[tex]\nabla\cdot\vec{E} = \vec{k}\cdot\vec{E} = 0[/tex]

Which shows that the wave vector is perpendicular to the field.

- #4

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