  We study a system of electrons moving on a noncommutative plane in the
presence of an external magnetic field which is perpendicular to this plane.
For generality we assume that the coordinates and the momenta are both
noncommutative. We make a transformation from the noncommutative coordinates to
a set of commuting coordinates and then we write the Hamiltonian for this
system. The energy spectrum and the expectation value of the current can then
be calculated and the Hall conductivity can be extracted. We use the same
method to calculate the phase shift for the Aharonov-Bohm effect. Precession
measurements could allow strong upper limits to be imposed on the
noncommutativity coordinate and momentum parameters $\Theta$ and $\Xi$.
