184_projects:multiple_induction [Projects & Practices in Physics]

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==== Project: Manny's Recycling ====
As the last of the reconstructed powerlines get put into place, the citizens of Lakeview have discovered that a strong magnetic field will temporarily stun the EM boar-tigers, allowing one to easily get to safety. Pooling together every last tax dollar, the citizens of Lakeview have decided they should create a constant 5 mT magnetic field everywhere in town to ensure the safety of their citizens.

However, the superstitious local named Manny Hallabero is peppering the Lakeview City Council with questions about the new magnetic field surrounding Lakeview. You see, Manny is a dedicated recycling enthusiast and has been collecting discarded wire coils from the Hawkion Detector. Manny was planning a large transport of the coils, along with some spare magnets and power supplies, but he is now concerned. He has constructed a variety of scenarios (though some seem a bit outlandish) and asked the Lakeview City Council for answers. Given your expertise, the Lakeview City Council has asked you to analyze each situation to determine: 1) is there an induced current in the given wire coil and 2) if so, what direction is the induced current?

=== Bar Magnet Situations ===
{{ 184_notes:induction1.png }}

=== Coil Situations ===
{{ 184_notes:induction2.png }}

=== Challenge Questions: Practice with Calculations & Graphs ===
{{184_notes:induction3.pdf}}

<WRAP Info>
=== Learning Goals === 
  * Use Faraday's Law to determine if there is an induced current
  * Draw dA vectors and determine change in flux for a coil
  * Use the RHR to determine the direction of induced current
  * Identify assumptions to simplify the magnetic flux integral
  * Identify steps needed to determine an induced current direction
  * Explain the difference between conventional current and induced current
</WRAP>

Conceptual Questions:
  - What assumptions are you making in these RHR problems? (Hint: particularly, what assumptions are you making about the B-field?)
  - What direction does the dA vector point? 
  - What would change about your answer if you picked the opposite dA vector? Select one of the scenarios above and fill out the table for both dA vectors - what changes and what stays the same?
  - How do you simplify the flux integral? (Hint: there are two key simplifying steps to simplify the integral!)
  - Is flux a vector or a scalar? How do you know? 
  - What makes flux positive or negative? When will flux be zero?
  - Out of all of your scenarios - what causes there to be no induced current? What patterns do you see across all the scenarios?