. Author manuscript; available in PMC: 2013 Nov 6.

Published in final edited form as: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 May 13;79(5 0 1):051908. doi: 10.1103/PhysRevE.79.051908

TABLE VI.

Spherical tank corrections to magnetic field of electric multipoles

Dipole

B_{s} (a_{10}) = \frac{1}{4 π} \frac{a_{10}}{2 r^{3}} (y \hat{x} - x \hat{y})

B_{s} (a_{11}) = \frac{1}{4 π} \frac{a_{11}}{2 r^{3}} (- y \hat{z})

B_{s} (b_{11}) = \frac{1}{4 π} \frac{b_{11}}{2 r^{3}} (x \hat{z})

Quadrupoles

B_{s} (a_{20}) = \frac{1}{4 π} \frac{3 a_{20}}{4 r^{5}} z (y \hat{x} - x \hat{y})

B_{s} (a_{21}) = \frac{1}{4 π} \frac{3 a_{21}}{4 r^{5}} [x y \hat{x} + (z^{2} - x^{2}) \hat{y}) - y z \hat{z}]

B_{s} (b_{21}) = \frac{1}{4 π} \frac{3 b_{21}}{4 r^{5}} [- (z^{2} - y^{2}) \hat{x} - x y \hat{y} + x z \hat{z}]

B_{s} (a_{22}) = \frac{1}{4 π} \frac{3 a_{22}}{2 r^{5}} [y z \hat{x} + x z \hat{y} - 2 x y \hat{z}]

B_{s} (b_{22}) = \frac{1}{4 π} \frac{3 b_{22}}{2 r^{5}} [- x z \hat{x} + y z \hat{y} + (x^{2} - y^{2}) \hat{z}]