Project 12
Project 12A: 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.
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.
Conceptual questions:
- What is the shape of the magnetic field due to a solenoid? (Inside the solenoid vs outside the solenoid?) How does that relate the magnetic field from a current coil?
- How did you pick your Amperian loop for the solenoid? How does your loop choice simplify Ampere's law?
- Would you want to pick an Amperian loop that is the same length as the solenoid? Why or why not?
- What assumptions did you make in this problem and why did you need to make them?
- Solenoids are highly used in real life when a magnetic field is needed. Why would solenoids be frequently used? What are they used for?