This question caused a debate in the class: EMF from a changing magnetic field

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The discussion centers around a debate in a class regarding the correct answer to a question about EMF induced by a changing magnetic field. Participants analyze the relationship between magnetic flux and induced EMF, referencing the relevant equation and discussing the graphical representation of these concepts. The consensus leans towards option A, as it is believed that the maximum EMF occurs when the magnetic flux is changing rapidly. Clarifications are made about graph labeling, particularly identifying point Q as significant in determining the correct answer. The conversation concludes with a sense of resolution regarding the understanding of EMF induction.
Physical_Fire
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Hello,
So recently our class have learnt about E.M.F induction entirely with it's equation and a classmate found a question from the internet. I honestly believe the answer is A as the magnetic field is changing rapidly, but some of my classmates believe it's B. While others believe it's C. This has caused a debate to ensue and I shared my reasoning. What does the community think is the correct answer?
1717688734147.png
 
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What is the Relevant Equation relating EMF to the magnetic flux through the coil? Can you sketch a plot of the magnetic flux versus time while the magnet is spinning (and label the points P, Q, R on that plot)?

And based on the Relevant Equation, what do you need to do to that plot to show the EMF induced in the coil versus time? :smile:
 
-d phi(b) / change in t. phi(b) is the change in magnetic flux. and the graph would be as attached. However, I am not sure how to label as I don't understand which has the highest emf
1717689686205.png
 
Good. The first vertical dotted line on the left is in the wrong place, though, and should be at the Origin (move it to the left).

Where do you think point Q could be on the graph?

EDIT -- the 3 middle points on the 2 graphs look okay, but the outer points are a bit misaligned (the bottom sine wave is asymmetrical)
 
Q should be the second vertical line as it has the magnetic flux is changing rapidly so emf is at its max. So does that mean it's A, and I was secretly right the entire time?
 
Physical_Fire said:
Q should be the second vertical line as it has the magnetic flux is changing rapidly so emf is at its max. So does that mean it's A, and I was secretly right the entire time?
It could be either of the zero crossings of the flux sine wave, so yes, I believe the correct answer is A.
 
Thanks for resolving.
 

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