184_projects:power_lines_2 [Projects & Practices in Physics]

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==== Project: Rebuilding Power Lines ====

{{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 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 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.

{{  183_projects:lakeview_wires_2_1.png?900  }}

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 Right Hand Rule to determine the direction of magnetic field.
  * Use Right Hand Rule to determine the direction of magnetic force.
  * Understand how the integral version of the magnetic field equation relates to the long wire equation.
  * 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?
  - If the wire has $0.008 \Omega/m$ resistance, how big of a power supply would be required for your current? (Calculate this!)
  - What would change about your solution if the currents went in the same direction instead of opposite directions?
  - What assumptions did you make in this problem? What are the limitations of your solution?
  - When do you want to use the integral form of the B-field equation? When can you use the long wire equation?
  - 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.)