The analytical magnetic field (including Lorentz Correction) produced
by a spherical object of radius and susceptibility inside
a medium of susceptibility is given by
Figure 1 show the field distribution (less ) along the axis of a sphere, comparing the analytical solution given in equation 28 with the solution calculated with the perturbation method. Figure 2 shows plots through the centres of these spheres for a range of different radii, mm, where in each case the voxel size is mm. This demonstrates the relationship between spatial extent and size of the error, where it can be seen that the maximum error is approximately equal to 1 ppm in all cases, with the spatial extent of significant errors covering 5 voxels or so. These results are very similar to those shown in [4,1,2,5] despite the range of different object models (e.g. boundary element methods vs voxels) and approximations used.