The present invention relates to a ground milling machine, in particular a road milling machine, for removing ground material, comprising a machine frame having a chassis, a milling drum supported on a machine frame, and a transport device having at least one conveyor belt, which is configured for conveying removed ground material in a conveying direction away from the milling drum to a discharge point, as well as to a method for operating a ground milling machine. One aspect of the present invention is to provide an electrostatic precipitator, which reduces the dust pollution.