  For an atomic condensate in an axially symmetric magnetic trap, the sum of
the axial components of the orbital angular momentum and the hyperfine spin is
conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field)
is not axially symmetric, the difference of the two becomes surprisingly
conserved. In this paper we investigate the relationship between the values of
the sum/difference angular momentums for an atomic condensate inside a magnetic
trap and the associated gauge potential induced by the adiabatic approximation.
Our result provides significant new insight into the vorticity of magnetically
trapped atomic quantum gases.
