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. 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 III.

Radial component of magnetic field and magnetic dipole moments

Dipole
B_r(a₁₀) = 0
B_r(a₁₁) = 0
B_r(b₁₁) = 0
Quadrupoles	Non-zero magnetic moments
B_r(a₂₀) = 0	None
$B_{r} (a_{21}^{1}) = - \frac{a_{21}}{4 π} \frac{y}{r^{4}}$	$B_{11}^{m} = a_{21} ∕ 2$
$B_{r} (a_{21}^{2}) = - \frac{a_{21}}{4 π} \frac{y}{r^{4}}$	$B_{11}^{m} = a_{21} ∕ 2$
$B_{r} (a_{21}^{3}) = 0$	None
$B_{r} (b_{21}^{1}) = - \frac{b_{21}}{4 π} \frac{x}{r^{4}}$	$A_{11}^{m} = b_{21} ∕ 2$
$B_{r} (b_{21}^{2}) = \frac{b_{21}}{4 π} \frac{x}{r^{4}}$	$A_{11}^{m} = - b_{21} ∕ 2$
$B_{r} (b_{21}^{3}) = 0$	None
$B_{r} (a_{22}^{1}) = \frac{a_{22}}{4 π} \frac{2 z}{r^{4}}$	$A_{10}^{m} = a_{22}$
$B_{r} (a_{22}^{2}) = - \frac{a_{22}}{4 π} \frac{2 z}{r^{4}}$	$A_{10}^{m} = - a_{22}$
$B_{r} (a_{22}^{3}) = 0$	none
$B_{r} (b_{22}^{1}) = \frac{b_{22}}{4 π} \frac{2 z}{r^{4}}$	$A_{10}^{m} = b_{22}$
$B_{r} (b_{22}^{2}) = - \frac{b_{22}}{4 π} \frac{2 z}{r^{4}}$	$A_{10}^{m} = b_{22}$
$B_{r} (b_{22}^{3}) = 0$	None