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Electric fields, magnetic fields and Lorentz frames 
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#1
Oct2106, 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.



#2
Oct2206, 11:31 AM

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PF Gold
P: 2,007

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



#3
Oct2306, 03:13 AM

P: 17

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



#4
Oct2306, 06:52 AM

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PF Gold
P: 2,007

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. 


#5
Oct2406, 01:44 AM

P: 17

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



#6
Oct2406, 08:44 PM

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PF Gold
P: 2,007

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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