1. **Beam experiment. Decades ago, we built a cheap experimental facility in the basement of FRH. We already had a big capacitor bank called a Marx generator that went to high voltage when we closed its switches. We used the Marx generator to make an intense beam of ions and electrons called a neutralized ion beam. The purpose of the experiment was to see how far the neutralized ion beam would travel when it entered a magnetic field of varying magnitude and direction relative to the beam. In the experiment, we tried to make the magnetic field spatially uniform; assume it is in your calculations. Figure 1 illustrates the apparatus. To make the axial field, we wrapped a thick wire around the long cylindrical chamber 50 times in a solenoidal configuration. The cylindrical chamber was 3.0 m long and 1.0 m in diameter. To make a vertical field, we mounted wires on a wooden structure; the seven wires were connected in series and carried current down one side of the cylinder and back on the other. The wooden frame was 1.2 m high, 1.2 m wide, and 3.2 m long. The maximum magnetic field that could be produced either vertically or axially was 0.025 T. The beam traveled axially down the chamber. (a) Although we could have used DC currents in our coils, if you only want a field for a short time, it's much cheaper to pulse on the magnetic field for a short time, so that's what we did. (We arranged the timing of the currents in the axial and vertical fields so the currents were nearly constant when we fired the neu- tralized beam. The beam only lasted about 1 us.) However, because we used pulsed power to produce the magnetic fields, the cylindrical vacuum chamber could not be metal; instead, we used a big sewer pipe made of fiberglass (an in- sulator) as our vacuum chamber. Qualitatively, in one sentence, why couldn't we use a metal vacuum chamber? (b) When we made an axial field, how much energy was stored in the field? When we made a vertical field, how much energy was stored in the field? (c) What was the inductance of the axial field coil? (d) What was the inductance of the vertical field coil? (e) What was the mutual inductance between the two coils? [Hint: consider 45.] SIDE VIEW END VIEW Figure 1: Illustration of the apparatus that made (approximately) uniform magnetic fields at different angles. A thick wire that spiraled around the cylindrical sewer pipe produced an axial field. A thick wire that was mounted on a rectangular frame produced the trans- verse field; the wire went all around the lowest rectangle first, then moved up to the next rectangular loop, then the next, etc. (f) In each circuit, we used an L-C circuit to drive the current in the coil. First, we would charge a capacitor to 30 kV. Then we would fire a switch to connect the capacitor to the coil, as in the can crusher demonstration. Assuming no energy is dissipated, what capacitance did we need for the axial field circuit? For the vertical field circuit? (g) We fired the beam when the currents in the coils were at their maximum values. If the beam was fired at = 0, how much earlier did we need to close the switch on the axial-field circuit? On the vertical-field circuit? (h) Qualitatively, why did we use thick copper wires in our field circuits