700. Suppose you have two electric currents, one consisting of electrons and the other of protons, moving in the same direction at the same velocity. Will the magnetic fields that these currents produce have identical magnitudes and directions? The right hand rule describes the direction of the magnetic field in terms of the direction of current, so it appears that it should be independent of the current's charge. — ABD, Petersburg, VA
Current is defined as flowing in the direction of positive charge motion. Because electrons are negatively charged, the current they are carrying is flowing in the direction opposite their motion! In your question, you describe two beams, one of electrons and one of protons, and note that both beams are heading in the same direction at the same speed. The proton beam's current is heading in the same direction as the beam while the electron beam's current is heading in the opposite direction from the beam. Assuming that the two beams have equal numbers of particles per second, they will produce magnetic fields of equal magnitudes. But the magnetic field produced by the electron beam will be directed opposite that of produced by the proton beam!
A beam of hydrogen atoms—each of which consists of one proton and one electron—is a perfect example of this situation. The electrons in that atomic beam produce a magnetic field in one direction while the protons in that atomic beam produce a magnetic field in the opposite direction. The two fields cancel one another perfectly, as they must because a beam of neutral hydrogen atoms can't produce any magnetic field.