Word is starting to get out about your teams increasing expertise in electricity and magnetism. The mayor, Virginia Bernera, of nearby Springfield has reached out to you and your team to consult about a recent problem with the town's power lines. A few nights ago, after curfew, something came through the town and tore down all the power lines, including the transformer for the incoming transmission line from Lakeview. Whatever it was, all the wires are chewed up and torn, and there are deep claw marks on the utility poles, which luckily are still standing. Nobody in the town seems to know what happened, and the residents of Springfield are pretty spooked. In any case, the mystery can wait for another day – Springfield needs its power back as soon as possible.

There is an incoming transmission line on the edge of Springfield from which you need to set up the power lines that will run through the whole town. Mayor Bernera has supplied you with some specifications: Each power line will be erected to connect the transformer from the incoming transmission line to the homes and businesses in Springfield. Each line is $5 \text{ km}$ long and is made of a metal alloy with $0.008 \text{ $\Omega$/m}$ of resistance.

The most important decision in this reconstruction process is to determine which transformer to install at the incoming transmission line. A given transformer will create a specified voltage drop from the transmission to the residential area. However, there are some risks associated with your choice. One risk is that the electric field along the line will heat up up the wire and cause it to melt, which will happen when the electric field reaches $3 \text{ kV/m}$. Another risk is that the line may create a magnetic field on the ground that is dangerous for people walking around and may interfere with portable electronics. The safety limit for the magnetic field is $10 \text{ mT}$.

You have three options for your choice of transformer. The voltage drop on the line from the functioning transmission line to the residential area can be $1 \text{ MV}$, $10 \text{ MV}$, or $100 \text{ MV}$. Evaluate each decision and produce a recommendation based on the safety concerns and the power that the transformer will produce for Springfield.

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After you complete the power lines in Springfield, you stick around to talk to the locals about what could have caused such extensive damage. Finneginn Flaherty, the local baker, spotted a giant creature flying through the air and emitting large sparks. It seemed like the creature became momentarily stunned when it flew close to the powerline, after which it tore them down with a vengeance. Now that your team has re-established communication with Lakeview, you call your colleagues at the Hawkion Detector and tell them what you have learned. They hypothesize that these could be the same creatures that caused problems with the wildlife around Lakeview. They also think that the magnetic field caused by the current through the power lines may be what seemed to stun the beast.

The research team at the Hawkion would like to study the creatures more closely and suspect that the creatures are still in the Springfield area but will soon return to the nearby lake to feed on the fish and birds. (Perhaps a solution to Dr. Taulest's mystery?) They have asked you to help them create a strong, constant magnitude, constant direction magnetic field along the whole eastern edge of the lake. They are hoping this field will stun at least one of the creatures as they are traveling from Springfield to the lake. Since it is unclear yet whether the creatures can fly or not, the research team does not expect you to stun and catch all of the beasts, but they are confident that if you can produce a strong constant magnetic field that occupies at least 2 meters vertically, there is no way all of the creatures can dodge it when they travel to the lake – you will be sure to capture at least one for research.

Since the Hawkion researchers have generously donated all of the extra copper wire, one of your colleagues has suggested creating a giant solenoid (2 m in diameter, 1 km long) to create such a magnetic field. They claim that if you use the power supply/current from the Hawkion Detector and design the solenoid right, they can create a $10 mT$ magnetic field that will definitely stun the creatures. Your boss has you as the E&M experts to work out what the solenoid would need to look like and if it is feasible to create before they invest all their time/materials in creating such a solenoid. */