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?