- #1

castlemaster

- 38

- 0

## Homework Statement

We have an homogeneus electromagnetic field with [tex]E \bullet B=0[/tex] and [tex]E \neq cB[/tex]

Find the velocity of the reference frames in which ony E exists.

## Homework Equations

[tex]\mathbf{E}' = \gamma \left( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right ) - \left (\frac{\gamma-1}{v^2} \right ) ( \mathbf{E} \cdot \mathbf{v} ) \mathbf{v}[/tex]

[tex]\mathbf{B}' = \gamma \left( \mathbf{B} - \frac {\mathbf{v} \times \mathbf{E}}{c^2} \right ) - \left (\frac{\gamma-1}{v^2} \right ) ( \mathbf{B} \cdot \mathbf{v} ) \mathbf{v}[/tex]

## The Attempt at a Solution

I guess I can't use the transformations for a boost in the x direction, so I guess I have to use the fact that

[tex]E \bullet B[/tex]

[tex]E^2-B^2[/tex]

are invariants under lorentz transformations.

But I don't know how to start. Do I need the EM field tensor for something?

Thanks