Magnetic Field And Field Gradient Corrections within a Nonconducting Sensor Enclosure in a Conducting Fluid---Part III: Current Exclusion Contribution for an Arbitrary Axisymmetric Enclosure

Neglecting the velocity field perturbation, we examine the current exclusion contribution to the magnetic distortion field /
^→
_H
/' along the symmetry axis of a "streamlined" enclosure in the shape of a general body of revolution. In contrast to the case of a spherical enclosure where all orientations of the (unknown) unperturbed current density /
^→
_J
/
₀
relative to the enclosure surface are equivalent, for the present geometry the relative orientation of /
^→
_J
/
₀
must be specified. On the symmetry axis (z-axis) the component of the distortion field parallel to that axis vanishes independent of the orientation of /
^→
_J
/
₀
. In regard to field gradients, all diagonal elements of the gradient dyad similarly vanish. However, only the combination ∂H'
_x
/∂y + ∂H'
_y
/∂x vanishes independent of orientation. Here (x, y) denote any two orthogonal directions perpendicular to the symmetry axis.