184_projects:f20_project_10 [Projects & Practices in Physics]

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===== Project 11 =====
 ==== Project 11A: Rebuilding Power Lines ====

{{183_projects:powerlines.jpeg?600}}

Despite the magnetic field, the EM-Boar tigers are causing all sorts of problems. Last night, one of them came through Lakeview and tore down all the power lines, including the transformer for the incoming transmission line from the power plant on the edge of town. All the wires are chewed up and torn, and there are deep claw marks on the utility poles, which luckily are still standing. The residents of Lakeview are pretty spooked. Lakeview needs its power back as soon as possible.

There is an incoming transmission line on the edge of town from which you need to set up the power lines that will run through all of Lakeview. The manager of the power plant, Dr. Erma Cürd, 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 Lakeview. 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 Lakeview.

<WRAP info>
===Learning Goals===
  * Use Ampere's Law to calculate the magnetic field outside of a current-carrying wire.
  * Explain why you pick your Amperian loop and how it helps you simplify your calculations.
  * Explain the general steps that you take when using Ampere's Law.
  * Explain what would change about your solution if the wire were coaxial (this part is extra).
</WRAP>


==== Project 11B: Set Your Solenoids to Stun ====

As the last of the new power lines were assembled the town can finally try to enact its escape plan. The townsfolk with the support of the S.P.A.R.T.A.N task force have been secretly constructing a subway in order to evacuate the town from the omnipresence of the storm cloud.

Now that the power is back on, the people of Lakeview are itching to use this subway system to escape. Before the town opens up access to the subway system, Lakeview's general manager of transportation, Dr. Hawk Natkins, has asked you to go underground and make sure everything seems safe.

You and your team comply and descend into the subway system. You notice a bright blue glow coming from deep in one of the subway tunnels... Yup, it's definitely a pack of hungry EM-boar tigers, ready to munch on a subway car or something. You immediately radio up to Dr. Natkins to see what you should do. He explains that from their previous experiences with EM-boar tigers they become frightened by a magnetic field of 5mT. He also tells you the wiring embedded in the walls of the subway tunnel are arranged just like a big solenoid.

The tunnel is 1 km long, and Dr. Natkins estimates there are about 8,000 coils of wire from one end of the tunnel to the other. Based on from what you can see right now, the tunnel looks to be about 10 meters wide. Dr. Natkins says that if you can tell him a value for the current needed in the solenoid's wire, he will relay the value to Dr. Cürd over at the power plant, and she will be able to set the current to the desired value to produce a magnetic field. Your job is to figure out what value of current you'd like to relay to Dr. Natkins, and why this will produce a big enough magnetic field to scare off the EM-boar tigers.

{{ 184_notes:em_boar_tunnel.png?600 |Uh-Oh}}

<WRAP info>
===Learning Goals===
  * Use Ampere's Law to calculate the magnetic field inside a solenoid.
  * Explain why you pick your Amperian loop and how it helps you simplify your calculations.
  * Explain the general steps that you take when using Ampere's Law.
  * Practice using a differently shaped Amperian loop, or figuring out the enclosed current for more than one wire.
</WRAP>