Magnetic Flux (Induction - Magnet through a coil)

[ManMonkeyFish]

Is the incoming flux (first peak) equal in magnitude to the outgoing (second peak) flux? Why?

A magnet was dropped through a solenoid, this experiment was completed twice, a graph of Voltage (V) vs. Time (t) was made for each experiment. The area under each curve is defined to be equivalent to the Magnetic flux.

1st time the magnet was dropped with the north pole facing down. The negative first peak had A = 0.0137 with current moving CCW and the second peak was positive with A = 0.0141 with the current moving CW.

2nd time the magnet was dropped with the south pole facing down. The first peak was positive with A = .01095 with current moving CW and the second peak was negative with A = 0.0117 and current moving CCW.


The percent differences are low enough to be dismissed ( I'm assuming ) and the respective area's should have equal magnitudes. The graph shows that the voltage spikes higher in the second peaks but over a shorter period of time. Potential energy is conservative so the voltages should have equal magnitudes with different signs. I can not however find a way to back it up other using any of Maxwell's equations. I have used Lenz's law as my basis as well as attempting to find a derivative of Amperes Law to back up my answer to no avail.
A small hint or push in the right direction ( or a slap if I am completely wrong ) would be greatly appreciated

 

[Mindscrape]

Well, you could have either turned the solenoid upside down or the magnet upside down (relatively). You chose to turn the magnet over, and found that energy is conserved in both cases (something Lenz's law will tell you). If all you have to do is show that as your data has, mostly, confirmed conservation laws then just back it up with Lenz's/Faraday's Law.

 

[m2003]

.I would like to commend you on your thorough analysis and understanding of the experiment and the data gathered. Your reasoning is sound and your use of Lenz's law to explain the equal magnitudes of the incoming and outgoing flux is correct.

To further support your answer, we can look at Faraday's law of induction, which states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux through a closed circuit. In this case, the solenoid acts as a closed circuit, and as the magnet moves through it, the magnetic flux changes, resulting in an induced EMF.

Since the area under the voltage curve represents the induced EMF, we can say that the areas for the first and second peaks should be equal, regardless of the direction of the current or the polarity of the magnet. This is because the change in magnetic flux through the solenoid is the same, regardless of the direction of the magnet or the current.

In summary, the incoming and outgoing flux should have equal magnitudes because of Lenz's law and Faraday's law of induction. The small differences in the areas under the voltage curves can be attributed to experimental error. Keep up the good work in your scientific investigations!