# Electric fields, magnetic fields and Lorentz frames

1. ### golfingboy07

17
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. ### Meir Achuz

2,059
Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.

3. ### golfingboy07

17
ok. would you be able to start me off though?

4. ### Meir Achuz

2,059
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. ### golfingboy07

17
yes i know what the F tensor is in terms of the components of E and B

Last edited: Oct 24, 2006
6. ### Meir Achuz

2,059
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