Faraday's law help -- Induced EMF vs. time graph

[sdfsfasdfasf]

Homework Statement

I need help deducing whether my textbook is wrong or not.

Relevant Equations

E = -N d(phi)dt

Here is a curve of induced emf against time. We know from Faraday's law that E = -N d(phi)dt and due to the negative sign, clearly E and d(phi)/dt must have opposite signs, i.e if E > 0it would not be possible for d(phi)dt > 0, as then -N d(phi)dt = E <0 , when we already defined E >0, clearly a contradiction. You can clearly see that from t=0 to just after t=0.1, E > 0, therefore d(phi)dt < 0. However my solution from the textbook states that initially the flux linkage (N phi) increases, which means that N d(phi)dt >0, which is direct contradiction as clearly E > 0 at the start. Posted the solution down below.

 

[kuruman]

You did not describe the physical situation that is taking place. If you have a magnet falling through a coil, the polarity of the induced emf will depend on whether the north pole is leading or trailing.

 

[sdfsfasdfasf]

 

[kuruman]

I used to own a torch like that. You have to understand that the polarity of the pulse is relative and depends, as I said, on whether the north pole of the magnet is leading or trailing and on which side of the voltmeter measures the emf pulse is connected to which side of the coil. You reverse one or another, the polarity is reversed. You reverse both, the polarity stays the same.

Look at the schematic on the right. The red wire is behind the coil and the blue wire is in front of the coil. When the magnet falls as shown, magnetic field lines point down and are increasing. The induced current will be opposing the down increasing magnetic field lines by creating magnetic field lines that are up. This means that current will flow from blue wire to red and from point A to B charging the capacitor and lighting up the LED.

When the magnet is below the coil, the magnetic field lines are still down but are decreasing. This means the current must flow in the opposite direction from before (B to A) to oppose to increase the decreasing magnetic field lines.

All this will be reversed if you flip the falling magnet upside down. Your drawing does not show which pole is leading.

 

[sdfsfasdfasf]

While being the highest level before university (A-Level, here in the UK), my physics course is still fairly introductory, it is extremely common for them to miss out "crucial" information when writing questions as it is not really required to answer the question (usually) and they need the exam to be a good fit for all students, from those who get 5% to those who get 95%. All in all, I am generally not very comfortable with electromagnetism because I feel as though the textbook does not do a good job of teaching it. Do you have any Pre-University Physics Electromagnetism resources? Thanks

 

[haruspex]

It is not clear to me whether the two explanations ("because: …. or ….") are intended to be equivalent statements of fact or a question for the reader to answer. If the first, I agree it is wrong, but if the second, you have answered it.

 

[sdfsfasdfasf]

This screenshot is from the worked solution, everything that is written is meant to be true fact (if the author has done a good job), so it seems to me that the two explanations are both meant to be true. In that case surely something is off right?

 

[haruspex]

Your drawing does not show which pole is leading.

@sdfsfasdfasf's point is that the text says "… e.m.f. changes from positive to negative because … the flux increases then decreases." That statement in itself appears at odds with Lenz's law. (I read that Lenz added the minus sign.)
The sign must be based on some convention about which way the emf is measured and, perhaps, which way the coil is wound, but I have not been able to track down a statement of either.
Maybe Faraday used an opposite convention, and the quoted textbook uses that too.