Electric field in a rotating frame

[Malamala]

Hello! I have a radially pointing electric field i.e. at a given radius, R, the electric field has the same magnitude and points radially around that circle of radius R. I have a particle moving around that circle of radius R, with uniform velocity (ignore for now how it gets to move like that). What is the field felt in the rest frame of the particle (assume that z-axis is the same for the lab and particle frame)? Will it be a constant field always pointing along the same direction, or will it appear as a superposition of 2 oscillating fields, one in x the other in y direction, out of phase by $\pi/2$ (basically like an electric field rotating in the x-y plane in the frame of the particle)?

 

[anuttarasammyak]

In the approximation that speed of the particle v << c, the direction of thus designed electric field, and centrifugal force in addition, coincide with r, the radical direction of the reference frame of rotation. If v is comparable to c, we must consider relativity and that might be messy.

Will it be a constant field always pointing along the same direction, or will it appear as a superposition of 2 oscillating fields, one in x the other in y direction, out of phase by π/2 (basically like an electric field rotating in the x-y plane in the frame of the particle)?

To reply we may need more information how you set not r and $\phi$ but x-axis and y-axis in the rotating frame of reference.