- 290

- 0

then we have this equations

[tex]\Delta\vec{E}-\frac{1}{c^2}\frac{\partial^2 \vec{E}}{\partial t^2}[/tex]

[tex]\Delta\vec{B}-\frac{1}{c^2}\frac{\partial^2 \vec{B}}{\partial t^2}[/tex]

Particular solutions of this equation

[tex]\vec{E}=\vec{E}_0 e^{i(wt-\vec{k}\cdot\vec{r})}[/tex]

[tex]\vec{B}=\vec{B}_0 e^{i(wt-\vec{k}\cdot\vec{r})}[/tex]

If we have coordinate frames [tex]S,S'[/tex]

System [tex]S'[/tex] has relative velocity [tex]\vec{u}[/tex] in [tex]x[/tex] direction compared with [tex]S[/tex]

System [tex]S'[/tex]

[tex]\vec{E}'=\vec{E}_0' e^{i(w't'-\vec{k}'\cdot\vec{r}')}[/tex]

[tex]\vec{B}'=\vec{B}'_0 e^{i(w't'-\vec{k}'\cdot\vec{r}')}[/tex]

System [tex]S[/tex]

[tex]\vec{E}=\vec{E}_0 e^{i(wt-\vec{k}\cdot\vec{r})}[/tex]

[tex]\vec{B}=\vec{B}_0 e^{i(wt-\vec{k}\cdot\vec{r})}[/tex]

Why phase

[tex]wt-\vec{k}\cdot\vec{r}[/tex]

must be invariant?