Conducting loop rotating in a magnetic field

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A bar magnet falling through a conducting wire loop induces current based on the principles of Faraday's Law and Lenz's Law. As the south pole of the magnet approaches the loop, the magnetic flux through the loop increases, leading to an increase in current. The direction of electron flow in the loop will be counterclockwise due to the orientation of the magnetic field lines. In a separate scenario, as the speed of a conducting loop rotating in a magnetic field decreases, the magnitude of the induced current also decreases. Understanding these concepts is crucial for solving related electromagnetism problems.
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A bar magnet falling vertically through a stationary horizontal loop of conducting wire. Then, there are two questions related to this problem.
1. As the south pole of the magnet approaches the loop, the current in the loop
1) decreases 2) increases 3) remains the same

2. As the south pole of the magnet approaches the loop, the direction of the electron flow in the loop is
1) counterclockwise 2) clockwise 3) alternating

3. Now this is a separate problem. As the speed of a conducting loop rotating in a magnetic field decreases, the magnitude of the induced current in the loop.
1) decreases 2) increases 3) remains the same

For me, I have no clue of solving these problems. I am weak at electromagnetism. I hope you can give me some hint and guide me to solve them. Thanks.
 
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You will want to review material on Faraday's Law and Lenz' "Law"; the latter is helpful in figuring out how (though, not in understanding why) the induced current will flow in the wire loop.

For the first pair of questions, consider that the bar magnet has its magnetic field lines emerging from its north pole and re-entering at its south pole. The "density" of magnetic field lines becomes larger closer to the poles.

As the south pole approaches the wire loop, more and more field lines are passing through it (we say the magnetic flux through the loop is increasing). Because this is the south pole, the field lines are pointing away from the loop. What do the two Laws mentioned above suggest will happen in the wire?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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