0

I have just been introduced to the concept of waves and I found this wave equation for an electromagnetic wave in a book. I don't understand what is $\vec{k}$ here.

$\vec{E}$ = $E°\vec{n}cos(\vec{k}.\vec{r})$

I don't think it is wave number since that can't be a vector. Kindly help! :)

Qmechanic
  • 220,844
Bread Butter
  • 3
  • 1

1 Answers1

3

This is a static field, so not really a wave. This however: $$\vec{E}=E_0\vec{n}\,\cos(\omega t-\vec{k}.\vec{r})$$ is a wave. $\vec{k}$ is called the wavevector:

  • its norm is the wave number
  • its direction is the direction of propagation

Take for example $\vec{k}=k\,\hat{x}$ and let $c=k/\omega$. Then: $$\vec{E}=E_0\vec{n}\,\cos(\omega t-kx)$$ This expression is invariant under $x\to x+l$ and $t\to t+l/c$ for any $l$, which means that this field propagates at velocity $c$ in the direction $x$.

Miyase
  • 6,342