Dono wrote:
On May 10, 10:01 pm, Tom Roberts wrote:
Dono wrote:
How can I find the transformation that ties E,B,E',B'? Any reference
that you can suggest? Thank you.
Look up the Faraday two-form (its dual is called the Maxwell 2-form or
tensor). Its components, when projected onto an inertial frame, consist
of the 3-vector components of E and B:

[ 0 -Ex -Ey -Ez]
F = [ Ex 0 Bz -By]
[ Ey -Bz 0 Bx]
[ Ez By -Bx 0 ]

Thank you, I know all this, I even wrote the transform in its
vectorial form. I asked something different, how does all this FURTHER
transform when frames S and S' are ROTATING with a constant angular
speed?

F is a tensor, so its components transform:
F_i'j' = dx^i/dx^i' dx^j/dx^j' F_ij
Compute dx^i/dx^i' for your rotation and apply. Note, however, that
interpreting those components in a rotating frame is non-trivial; in
particular I don't think the usual identification of them as components
of E and B applies. Indeed, I don't know what "E" and "B" mean in a
non-inertial coordinate system, and the only way I know to figure it out
is to relate them to E and B in an inertial system (so you're back where
you started).

IOW: this question is more complicated than how they transform, it is
also a question of what they mean.


Tom Roberts