On May 11, 12:04 am, Dono wrote:
We know that E and B transform as follows for S and S' moving with
relative speed V :

E'=E
B'=B for the components of E,B along the direction parallel with V

and

E'=gamma(V) (E+VxB)
B'=gamma(V) (B=VxE/c^2) for the components of E,B along the direction
perpendicular to V

Now, imagine that the axis x,y are rotating with the uniform angular
speed omega in the plane x-y while S' moves with uniform speed V along
the common axis x.
How can I find the transformation that ties E,B,E',B'? Any reference
that you can suggest? Thank you.

Dono****o, the problem you've set up is
physically meaningless. The frames S and S'
have been left void. Where is the source of that
electric/magnetic field located? Is it at rest in frame
S' or in S. Which is the rest frame for that source,
Dono****o? Is that source's rest frame rotating?
Or is it that you have a third different frame S''
implicitly involved, where the source of the field
is at rest?