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(a) A stream of charged particles is being injected along the +y-direction into a space that contains a uniform magnetic field in the +x-direction. The particles all have the same speed, but some of them are protons, some are alpha particles (consisting of 2 protons and 2 neutrons), and some are electrons. Qualitatively, how do the protons, alpha particles, and electrons move once they are injected into the field, and how do these motions compare with one another? (b) In a certain region of space, a constant electric field points in the +z direction and a constant-magnetic field points in the +y direction. A charged particle with charge q and velocity v passes-through the region undeflected. What does this tell us about the velocity v? Would charged particles with (1) other charges but the same velocity or (2) arbitrarily chosen charges and-velocities also pass through without deflection? (c) You are given a length of wire and a battery and told to form one or more current loops (without cutting the wire) in a region containing a constant magnetic field so as to create maximum torque.How do you do it? (d) Two long wires carrying current in the same direction run parallel to one another a distance dapart. If we fire charged particles along a path that runs directly in between the two wires and is parallel to them, will the particles be deflected? (Does it matter in which direction we fire the particles?) What if we rotate the path of the charged particles within the plane that is equidistant from the two wires? (e) A number of narrow wires are bundled together into a larger cable. The individual wires carry different currents in one direction or the other. What must be true about the currents collectively if we measure the integral ofB dot ds around the outside of the cable and find that it is non-zero?If we find that the integral of B dot ds around the outside of the cable IS zero, does this mean thatthe magnetic field everywhere around the cable is zero?

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