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.