1. What is the equation for magnetic force on a current wire? How is it similar/different from the magnetic force on a point charge?
2. What is the equation for magnetic field produced by a very long wire? When would you want/need to use the integral version and when is it ok to use the long wire equation?
3. If you use the magnetic field equation for a long wire, how do you determine the direction of the magnetic field?

There's good news and bad news in Lakeview. Dr. Triste's theory was correct, and the FTOE scientists were able to use the Hawkions to finally get rid of the storms! But last night, just as everyone was celebrating, a horde of giant creatures stampeded through the town, damaging buildings, leaving deep gouges in the utility poles with their claws and chewing up most of the power lines. Manny Habañero claims these are the creatures he's been warning everyone about, which he calls “boartigers.” He says they evolved after the War and have lived in the nearby mountains ever since, but he thinks that the Hawkion research at FTOE has somehow given them strange electromagnetic properties.

Needless to say, the residents of Lakeview are pretty spooked, and need their power back as soon as possible. Fortunately, there is a power plant near 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 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 µT.

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.

1. In order to simplify $\vec{F} = \int I d\vec{l} \times \vec{B}$ to $F = ILB$ there are several critical steps that you have to take. What are those steps that you need to simplify the force equation?
2. 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?
3. If the wire has $0.008 \Omega/m$ resistance, how big of a power supply would be required for your current? (Calculate this!)
4. What would change about your solution if the currents went in the same direction instead of opposite directions?
5. What assumptions did you make in this problem? What are the limitations of your solution?
6. 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.)