Noncommutative magnetic moment of charged particles

It has been argued that in noncommutative field theories, the sizes of physical objects cannot be taken smaller than an "elementary length" related to noncommutativity parameters. By gauge covariantly extending field equations of noncommutative U(1) theory to cover the presence of external sources, we find electric and magnetic fields produced by an extended static charge. We find that such a charge, apart from being an ordinary electric monopole, is also a magnetic dipole. By writing off the existing experimental clearance in the value of the lepton magnetic moments for the present effect, we get the bound on noncommutativity at the level of 104TeV.