# Electromagnetic field transformations under rotations

If you have magnetization vector in vertical magnetic field, it starts precessing. If you do a transformation to rotating coordinate system you obtain a stationary magnetization. Is there a direct formula to see that magnetic field is zero?

I understand that under transnational changes (e.g. motion along $x$) electric and magnetic field behave as: \begin{align} & E'_x = E_x & \qquad & B'_x = B_x \\ & E'_y = E_y - v B_z & & B'_y = B_y + \frac{v}{c^2} E_z \\ & E'_z = E_z + v B_y & & B'_z = B_z - \frac{v}{c^2} E_y . \\ \end{align} The easyest way to derive it is to consider Lorentz transformation of the $A^\mu$ and take $\gamma \to 1$ limit.

Is there analogous formula for rotation?

This is the closest I found on SE but it doesn't answer my question.

• A rotating coordinate basis is not stationary and there is no single rotation one can do to make it so. You would have to perform an infinite number of rotations for all points in time, but then you would not be in an inertial frame. Am I missing something? Jul 5, 2016 at 2:22