You are a particle physicist at the Large Hadron Collider who is tasked with designing an apparatus to separate annihilation pro
ducts (such as pions) from proton-antiproton collisions. Because positive and negative charges deflect differently in a magnetic field, you plan to use a magnetic field to separate these products. As a starting point, in which you ignore interaction effects and assume a known velocity, you decide to explore a beam of coincident positively and negatively charged pions, each of mass in and charge +lel and -del, respectively. These pions travel between two square sheets of a known number N of densely-packed parallel current-carrying wires, each of length L and individual current 1. Determine whether the currents in the different sheets should be in the same or opposite direction to create a magnetic field between the sheets. Then, determine whether the pion beam should be parallel or perpendicular to the wires as it travels between the sheets. Ignoring fringing effects, how strong must the wire current be so that the pions are separated by a distance of one-hundredth of the sheet length as they exit the plates?
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