  The possibility of testing spatial noncommutativity via a Penning trap is
explored. The case of both space-space and momentum-momentum noncommuting is
considered. Spatial noncommutativity leads to the spectrum of the orbital
angular momentum of a Penning trap possessing fractional values, and in the
limits of vanishing kinetic energy and subsequent vanishing magnetic field,
this system has non-trivial dynamics. The dominant value of the lowest orbital
angular momentum is $\hbar/4$, which is a clear signal of spatial
noncommutativity. An experimental verification of this prediction by a
Stern-Gerlach-type experiment is suggested.
