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Electric fields, magnetic fields and Lorentz frames

by golfingboy07
Tags: electric, fields, frames, lorentz, magnetic
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golfingboy07
#1
Oct21-06, 11:52 PM
P: 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.
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Meir Achuz
#2
Oct22-06, 11:31 AM
Sci Advisor
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PF Gold
P: 1,991
Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.
golfingboy07
#3
Oct23-06, 03:13 AM
P: 17
ok. would you be able to start me off though?

Meir Achuz
#4
Oct23-06, 06:52 AM
Sci Advisor
HW Helper
PF Gold
P: 1,991
Electric fields, magnetic fields and Lorentz frames

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.
golfingboy07
#5
Oct24-06, 01:44 AM
P: 17
yes i know what the F tensor is in terms of the components of E and B
Meir Achuz
#6
Oct24-06, 08:44 PM
Sci Advisor
HW Helper
PF Gold
P: 1,991
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.


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