On May 10, 9:29*pm, 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?

Express x and y as a function of time then express Faraday's
components in that coordinate system.

Use http://mathworld.wolfram.com/RotationMatrix.html as a guide for
x(t) and y(t).