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--- 184_projects:power_lines_2 [2022/11/14 20:33] – created dmcpadden
+++ 184_projects:power_lines_2 [2023/11/17 13:56] (current) – dmcpadden
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 {{183_projects:powerlines.jpeg?600}}
-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.
+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 in town 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 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.
+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 surviving power lines between the cities to supply the much needed power. Using some old blueprints, she found that the two powerlines are 5 km long, separated by 1.5 m, and are 5.5 m off the ground. Shown in the figure below. Dr. Cürd has a few options to setting up the power plant - she can set the power plant to send 837 A, 1167 A, 1500 A, or 1833 A through the two power lines.
-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 $10 \text{ mT}$.
+{{  183_projects:lakeview_wires_2_1.png?900  }}
-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.
+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, otherwise the wire will break out of its housing. However, 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 $\mu T$.
+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 & electricians.
 <WRAP info>
 ===Learning Goals===
-  * Use Ampere's Law to calculate the magnetic field outside of a current-carrying wire.
+  * Use Right Hand Rule to determine the direction of magnetic field.
-  * Explain why you pick your Amperian loop and how it helps you simplify your calculations.
+  * Use Right Hand Rule to determine the direction of magnetic force.
-  * Explain the general steps that you take when using Ampere's Law.
+  * Understand how the integral version of the magnetic field equation relates to the long wire equation.
-  * Explain what would change about your solution if the wire were coaxial (this part is extra).
+  * Calculate the force from one wire on another.
 </WRAP>
 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} $?
+  - If the wire has $0.008 \Omega/m$ resistance, how big of a power supply would be required for your current? (Calculate this!)
-  - 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?
+  - What would change about your solution if the currents went in the same direction instead of opposite directions?
-  - How would you calculate the magnetic field inside the wire? What would change about your calculation?
+  - What assumptions did you make in this problem? What are the limitations of your solution?
-  - 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 the integral form of the B-field equation? When can you use the long wire equation?
-  - When do you want to use Ampere's Law and when would you want to use the Biot-Savart Law to find magnetic field?
+  - How does this relate to real power lines? Do we actually use 1000 A of current in real power lines? (You may have to do some googling here.)