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I found these equations for electromagnetic field conversion in inertial frame for non relativistic case. If I have permanent static magnetic field with 3 components $B_x, B_y, B_z$ and permanent electrostatic field with 3 components $E_x, E_y, E_z$ in inertial frame in vacuum with zero speed, then in another inertial frame with the speed $V$ along x axis, electromagnetic field B’and E’ will be:

$E’_x=E_x, E’_y=E_y+VB_z, E’_z=E_z-VB_y$

$B’_x=B_x, B’_y=B_y-\frac{V}{c^2}E_z, B’_z=B_z+\frac{V}{c^2}E_y$

Simple example, if there is an static electron, it produces only electrostatic field, no magnetic field at all. But if I am moving in relation to electron, then in my inertial frame electron will be moving and it will produce magnetic field and I will see both, electric and magnetic fields.

Is there similar equations for non-inertial frame? I am looking for simplest case, like vacuum, all fields are static, permanent in the non moving system and speed/acceleration is small (non relativistic case).

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