# Electric fields, magnetic fields and Lorentz frames

1. Oct 21, 2006

### golfingboy07

Not sure how to go about proving that if E and B are perpendicular in one Lorentz frame they are perpendicular in all Lorentz frames.

2. Oct 22, 2006

### Meir Achuz

Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.

3. Oct 23, 2006

### golfingboy07

ok. would you be able to start me off though?

4. Oct 23, 2006

### Meir Achuz

Do you know the tensor F in terms of E and B?
If you don't know that much, you can't start the problem.
Go back to the textbook.

5. Oct 24, 2006

### golfingboy07

yes i know what the F tensor is in terms of the components of E and B

Last edited: Oct 24, 2006
6. Oct 24, 2006

### Meir Achuz

Find the dual tensor
{\cal F}_{\mu\nu}=\epsilon_{\mu\nu\rho\sigma}F^{\rho\sigma}.
Then form the scalar
{\cal F}_{\mu\nu}F^{\mu\nu}.
This will be proportional to {\bf E\cdot B}.
My latex didn't work, so try to read the above. Sorry.

Last edited: Oct 24, 2006