Project: Lakeview's Mystery
Kick Off Questions
- How is the magnetic field equation for a current wire similar/different from the magnetic field equation for a point charge?
- How is the right hand rule for a current wire similar/different to the right hand rules from last week?
- As a part of the magnetic field equation, you have to determine the $d\vec{l}$. What does the $d\vec{l}$ represent? How do you know what direction $d\vec{l}$ points?
Main Problem
You've just received a phone call from the head of the Wildlife Tracking Foundation of Lakeview. Dr. O'Taulest has been reporting that they have recently had an unprecedented disappearance of their green-bellied canaries that like to roost in the cliffs overlooking the lake. Their most popular nesting area on the eastern edge of the cliffs is completely empty. It's almost like they decided to migrate 4 months ahead of schedule! The Wildlife Tracking Foundation is also reporting that the fish, especially those near the north-eastern bank of the lake, have suffered a sudden decrease in their population.
Manny Habañero has worked this into his latest conspiracy theory – he claims that not only are his weird new monsters causing the storms, they are here because they are attracted to the Hawkions produced at FTOE, and they have eaten all the fish and birds in the area. Dr. O'Taulest is getting sick of listening to Manny rant about his tigers or boars or whatever they are, and claims there's a much simpler explanation: it's all your fault! He says that the large power lines running to FTOE to power the Hawkion accelerator are the problem. Clearly, the magnetic field from the power line interfered with the green-bellied canaries (who rely on Earth's magnetic field for migration purposes), causing them to vacate the vicinity.
As consultants on the Hawkion project, you have been asked to kindly disprove Dr. O'Taulest's claims. The government does not need any more press about Lakeview getting out given the continued storm front inhabiting the town. To start, you go back and consult the handy-dandy blueprints you drew up when designing the transmission line.
Learning Goals
- Use the right hand rule to determine the direction of the magnetic field near a wire.
- Calculate the magnetic field from a wire segment with a current and explain the role of superposition in your solution.
- Explain what the pieces of the integral are ($d\vec{l}$, $\vec{r}$, and limits) and how you determined them for your solution.
- Relate the magnetic field from a current to the magnetic field from a single moving charge - explain how these are similar and/or different.
Wrap Up Questions
- What steps do you take to set up the B-field integral?
- How do you decide what the separation vector is for a current wire?
- How do you pick the bounds for the B-field integrals?
- What assumptions did you make in this problem? What are the impact of those assumptions on your solution?
- If you moved the origin, what would be the impact on your solution?
- If you moved the observation point, what would be the impact on your solution?