Flipping Tables
The magnetic field strength of Earth is approximately half a Gauss (or 5e-05 T). It varies somewhat in magnitude and direction depending on where you are in the world, but to keep things simple, let's assume that wherever you are, the field has that magnitude and points perfectly parallel to the ground.
You may be sitting at a table or desk right now. Whether you are or not, let's pretend you are, and let's also suppose (again to keep things simple) that your table has a length of 1.877 m and a width of 0.908 m. These happen to be the dimensions of a table in the Studio room. Let's also pretend you wrap a copper wire around the perimeter of your table (one single loop).
EMF 1
If you were to keep the whole table horizontal and spin it around 180 degrees around a vertical axis in 15 s at a constant angular speed, what would be the magnitude of the average induced emf around the copper wire?
Note that in all parts of this problem we're going to be asking for average induced EMFs, so you don't need to take any instantaneous derivatives. Something involving deltas would be fine (like delta flux over delta time).
Note also that we're considering the EMF induced in a loop, so it would be very appropriate to use Faraday's law here.
$emf = 0 V$
EMF 2
If you were to flip the whole table along the short side from flat to an angle of $\pi/6$ with respect to the ground in 15 s, what would be the magnitude of the average induced emf around the copper wire?
$emf = 7.6 \cdot 10^{-7} V$
EMF 3
If you were to flip the whole table along one side from flat to an angle of $\pi/4$ with respect to the ground in 15 s, what would be the magnitude of the average induced emf around the copper wire?
$emf = 1.66 \cdot 10^{-7} V$
EMF 3b
If you were to flip the whole table along one side from the previous angle of $\pi/6$ to an angle of $\pi/4$ with respect to the ground in 15 s, what would be the magnitude of the average induced emf around the copper wire?
$emf = 9.03 \cdot 10^{-9} V$
EMF 4
If you were to flip the whole table along one side from flat to an angle of $\pi/3$ with respect to the ground in 15 s, what would be the magnitude of the average induced emf around the copper wire?
$emf = 2.84 \cdot 10^{-7} V$
EMF 4b
If you were to flip the whole table along one side from the previous angle of $\pi/3$ to an angle of $\pi/4$ with respect to the ground in 15 s, what would be the magnitude of the average induced emf around the copper wire?
$emf = 2.84 \cdot 10^{-9} V$
