Case 3: $B^{(0)}(\mathbf{x}) = (0,1,0)$

 

This is the same as the previous case except all $x$'s and $y$'s are swapped.

 

Note that the single voxel solution, $F(\mathbf{x}';\mathbf{x})$, in a constant field does not involve the unprimed coordinates, $\mathbf{x}$. Solutions when the zeroth order field involves a linear spatial gradient can be found in Appendix B and do involve both primed and unprimed coordinates.