PhysicsLAB Amusing Problems
The Tree House

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In this episode, Dr. J aligns himself with the farming community when he tries to plow a magnetic field with an iron tractor. (Meditate on that one.) Seriously though, Dr. J is offered a beautiful little place to live out in the country, rent-free. It's actually a tree house in the boondocks, but when you are run out of town, anything looks good. Being attracted to the offer, Dr. J decides to go out on a limb and move in. SAP learns of his new domain and decides to play a trick on the good doctor. They place two concentric coils around the tree house, each with 100 turns. One coil has a radius of 2 meters, while the other has a radius of 7 meters. They send a current of 5 amps through the outer coil, and they have the inner coil wired so that a current will run through it when Dr. J turns on his appliances. Since the tree house and Dr. J are located in the center of all this, a strong magnetic field should suddenly appear and rearrange things. However, it just so happens that Dr J turns on just enough appliances that the net magnetic field produced is zero. (I guess you could call it a lucky gauss!!)
 
What was the current in the inner coil, and in what direction (with respect to the 5-A current) must have it been traveling?

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