Shifting magnetic field axis

Question

Considering the image below, I have magnetometer readings while my magnetometer is oriented along x' and y'. Can I convert these readings to get the equivalent reading if my magnetometer was oriented along x and y.
$theta$ is known and the field I am trying to measure is the geo-static field in a closed environment.

Vincent Thacker · Accepted Answer

Yes, to find the components of the magnetic field $B$ in the new coordinate system, you simply have to apply a rotation matrix
$$begin{bmatrix} B'_x  B'_y end{bmatrix} = begin{bmatrix} costheta & sintheta  -sintheta & costheta end{bmatrix} begin{bmatrix} B_x  B_y end{bmatrix}$$

Mark H · Answer

Yes. A magnetic field is a vector field, so you can rotate the coordinate system as you want. You'll have to incorporate the error in the angle measurement into the error analysis of the field measurement.
Even if you can't move the probe permanently, you might be able to temporarily move the probe around the magnet or the magnet around the probe to see that the readings change as you would expect from a simple rotation.

Shifting magnetic field axis

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