In this Crash Course video, from 5:57 to 6:15, I think the directions are mixed up, but I could be wrong. She says that when moving the magnet into the loop, the generated magnetic field is pointing upward. She says that therefore, the current will be moving clockwise along the loop. And she says when the generated magnetic field is pointing downward, the current will be moving counter-clockwise. But if you point your thumb in the direction of the magnetic field (up in the first example), using the right hand rule, shouldn't current be flowing counter-clockwise? And vice versa? I'm not sure if I'm getting this wrong because I'm not understanding Lenz's law or if the video is incorrect on the directions.
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$\begingroup$ It depends on which pole of the magnet points towards the loop. Lenz law is based on the law of conservation of energy. If the North Pole of the magnet is moved towards the loop, a North polarity is induced in the loop. If you disagree, let us assume to the contrary that a South polarity is induced. If it were so, the loop would continue attracting the magnet without us having to do any work. This means that we can build a perpetual motion machine. But we cannot build a perpetual motion machine! A contradiction! And hence a North Pole moving towards the loop induces north polarity and vice $\endgroup$– Kunal PawarCommented Apr 3, 2017 at 1:45
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$\begingroup$ -versa. Choose the directions of the current in accordance with the polarity you need. Another way to think about it would be flux. Moving a magnet towards the loop changes the flux. The loop doesn't like that. And hence it induces a current in such a sense (direction?) that it opposes the source that caused that change. In other words increasing flux would cause flux to be induced in the opposite sense, such that the net flux decreases. Decide the direction of the current accordingly $\endgroup$– Kunal PawarCommented Apr 3, 2017 at 1:48
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I think it should be "when moving the magnet into the loop, the generated magnetic field is pointing downward". This is how the generated current tries to resist the increase in magnetic field when the magnet moves upward into the loop.
Or we can think in this way. There are magnetic field lines going from the center radially outward from N to S. And the magnet being moving upward is just equivalent to the coil moving downward. By $\vec{F}=q\vec{v}\times \vec{B}$, the positive charges ($q$) in the wire (let's use positive charge as it is easier than considering electron, which will give the same end result) moving downward will experience a force to move in the direction so that the current is moving clockwise and this will generate a magnetic field pioint downward too.
