Film flow of an incompressible, electrically conducting fluid in a nonuniform magnetic field was discussed in the first report. The effect of the gradient of an applied magnetic field strength on the film flow was clarified. And it was found that the electromagnetic force which is induced plays the role of a weir. In this paper a rivulet in such a field is discussed. When the flow rate is reduced, the film becomes thin, and then it ruptures and forms dry spots or a rivulet. Rivulet is supported by a relatively weak surface tension, and therefore it is easily influenced by the lateral force as well as the streamwise one. It is found that the lateral force which is induced by an interaction of the magnetic field with the streamwise component of the eddy-current acts like a non-contacting nozzle or a diffuser. An experimental study is carried out with a rivulet of mercury. The distributions of its widths and the heights of it are measured and they are shown to be in qualitative agreement with those of analytical results.