It is shown that when a magnetic field is used to support neutral atoms against the gravitational force mg, the total curvature of the field magnitude B must be larger than m^2 g^2/(2 mu^2 B), where mu is the magnetic moment of the atoms. This limits the minimum confinement strength obtainable for a trapped atomic gas. It is also conjectured that the curvature must be larger than twice this value for a magnetic potential that varies in only one or two dimensions, such as an atomic waveguide.
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