Dusty plasmas contain charged dust grains which are much bigger than protons and usually carry high negative charges owing to preferential capture of electrons. These dust grains do not have a fixed charge, and perturbations in the plasma induce fluctuations in the grain charges owing to liberation or capture of additional electrons and protons. The dispersion relation for low-frequency, long-wavelength and nonresonant electromagnetic fluctuations in a multibeam dusty plasma is derived by taking into account the momentum loss of electrons and protons owing to dust charge fluctuations. When the charging and discharging effects conserve momentum between any two species, the modes become unstable provided that a normalized averaged drift velocity exceeds the Alfvén velocity. However, when the charging and discharging effects are more complicated, drift dissipative type modes are excited when the normalized averaged drift velocity is below the Alfvén velocity. These modes could generate spatial structures over a wide range from hundreds to tens of millions of kilometres in dusty cometary tails. The analysis could be applied to certain planetary rings and to a dusty interstellar medium.