A theoretical model is presented of electron suppression in negative ion sources using transverse magnetic fields. These fields are of short range across the plasma electrode aperture of the high-voltage beam accelerator. They divert the electrons onto biased collecting surfaces which reduce the extracted electron current by factors in excess of 100. The model describes the scaling laws of the electron suppression effect and also the changes this field has on the extracted negative ion current which can be enhanced by the presence of the magnetic field.