Conceptual Lenz's Law

[Rucap09]

Regarding Lenz's Law, could someone explain what happens right when the conducting wire passes the boundary of the magnetic field.

For example, in TBR example where you have a conducting loop entering a field, I took it to mean that as you enter the field and add more X's the loop continues to add more O's by generating a current.

1) Is the current increasing as the loop enters (loop gains 5 X's, makes 5 O's, loop gains 5 more X's, now mass 5 more O's so 10 O's in total relating to a larger current) or is it just the rate that matters? Again pretending with arbitrary numbers, if the loop is gaining 5 O's per second the loop will create a constant current of 5 X's even though the amount of O's are increasing inside the loop?

2) As the loop is exiting the field, TBR says it "Gains O's, creates X's". The text sort of implies this, but does this actually just mean that there's now a negative rate of change for the X's so you make more X's to keep the amount the same?

3) Once the loop leaves the field, you have all of these X's that you just built up to offset the loss in X's from the field, but now the current just stops. Isn't that also a huge magnetic flux since your seemingly going from lot of X's to nothing instantaneously?

In short....my head hurts. Any help appreciated 🙂

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[Saxappeal1]

So I understand the desire to want to understand the "above and beyond" when it comes to physics, especially since the last PS sections have been supposedly very difficult, but in my opinion, this goes way beyond the scope of the MCAT. Getting the answer and understanding it are amazing and great but that is just like me reviewing my "physics with calculus" notes on maxwell equations for the MCAT. While once in a blue moon there may be a question without the calculus application about Lenz's law, or even a passage about it, this question seems to be way too involved to even have an iceberg's chance in the underworld to show up on the MCAT, and even if they did the passage would aptly explain it so that no outside knowledge is necessary since this level of physics isn't listed on PS. But, don't let that stop you from finding the answer, just, if it were me, I wouldn't focus on it, and I did physics with calculus at my university and I have yet to see one application of anything not on AAMC lists applied to a passage to the point where you need to know stuff like this, except for a stray passage on cyclotrons and even that gave you all of the information you needed. Just my 2 cents though, sorry I couldn't answer the question, I studied Lenz's law but this seems to go way too abstract into it, I've never seen an application like this before.

 

[gettheleadout]

1) the magnitude of the current depends only on the rate at which the wire loop is moving into/out of the magnetic field (this is because current is determined by the electromotive force, and by Faraday's law the emf is determined by the time-derivative of the magnetic flux.) The current will be constant throughout the process of entry/exit of the field.

2 & 3) Note that while completely inside the magnetic field, the wire loop experiences no current. As it begins to exit the field, assuming the rate of motion of the wire loop has been constant since before entry into the field and remains constant, you are correct that the rate of change of the magnetic flux through the loop will be of the same magnitude as when the loop entered the field, but opposite in sign (and indeed negative). Now, because the current in the wire loop is only dependent on rate, if you plotted the current during field entry/exit on an x-y graph of time vs current, you would see a square wave; the current does start abruptly and end abruptly. However, looking at the flux through the loop as represented by the number of X's and O's becomes somewhat problematic when we consider the induced current to be "adding X's" or "adding O's." Notice the induced current is present even when the wire loop has only just entered the field; the field may flow through 1% of the area enclosed by the wire loop but because the induced current magnitude (and thus the induced field strength) only depend on the rate, there are now X's (or O's depending on which direction the static magnetic field is directed) present throughout the entire area enclosed by the wire loop. The key point here is that the induced field is directed such that it acts to oppose the change in flux through the loop, but the net flux does not remain constant (and think, if it did, why would any current flow at all?). So the point is it's not as if the induced current in the wire is "adding X's/O's" at a constant rate during entry/exit of the external magnetic field; the flux from the induced field appears simultaneously with the start of the induced current. The result is that there is indeed a significant net flux through the loop that abruptly disappears just as the current abruptly stops. That said, this is no different from the abrupt loss of flux when a current loop powered by a voltage source is broken.