The dispersion properties of low frequency electrostatic modes in a dusty plasma in the presence of a static homogeneous magnetic field are examined. It is found that the presence of the dust particles and the static magnetic field have significant effects on the dispersion relations. For the parallel propagation the electrostatic mode is slightly modified by the magnetic field for the ion acoustic branch. A new longitudinal mode arises at the extreme low frequency limit, which is unaffected by the magnetic field for the parallel propagation. For the transverse propagation the ion acoustic mode is not affected by the magnetic field. However, the undamped extreme low frequency mode is significantly modified by the presence of the magnetic field for the propagation transverse to the direction of the magnetic field. (author). 23 refs.