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Project: Rebuilding Power Lines
Despite your best efforts to return the cub, the EM-Boar tigers around Lakeview have started causing all sorts of problems. Last night, one of them came through Lakeview and tore down all the power lines. 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.
Fortunately, there is a power plant by Springfield that is willing to help out the citizens of Lakeview. The manager of the power plant, Dr. Erma Cürd, has said that she can use two existing 5 km power lines between the cities to supply the much needed power. She can set the power plant to send 1167 A, 1500 A, or 1833 A through the two power lines. Shown in the figure below.
In talking to the Lakeview citizen's council, they are concerned that that the power lines will create a magnetic field on the ground that is dangerous for people & may interfere with portable electronics. They have required that magnetic field on the ground be less than 30 $\mu T$. Similarly, the lakeview electricians are concerned about the power lines themselves. They are concerned that the force from one wire on the other will end up moving them out of place. They have suggested that the force from one wire on the other must be under 1000 N to stay in place.
The city of Lakeview needs your help! Evaluate the current options and produce a recommendation for Dr. Cürd based on the safety concerns of the Lakeview citizens.
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).
Conceptual questions:
- In your calculations, you used dl or L a couple of times. What equations did you use with lengths, and which lengths were they referring to?
- What steps did you need to take to simplify the $\int \vec{B} \bullet d\vec{l} $?
- How did you pick your Amperian loop? Would a square Amperian have worked for the power line? Would a circle that is off center work?
- How would you calculate the magnetic field inside the wire? What would change about your calculation?
- If you had two power lines side by side, how would you find the force from one wire on another?
- When do you want to use Ampere's Law and when would you want to use the Biot-Savart Law to find magnetic field?