EMF v time graph vs change in flux v time

[alv]

I'm actually a teacher and I can't explain this problem from the 2007 HSC. I've attached a copy of the question and the two graphs. The question shows a graph of change in magnetic flux vs time and asks you to choose which graph of induced emf best fits it. I don't understand why the induced emf is at max even while the change in flux increases (or decreases).

I've searched for help on this but can't find it. I'd appreciate any explanation you could give me.

Thanks

Homework Statement

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Homework Equations

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The Attempt at a Solution

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[ehild]

emf= -ΔΦ/Δt, more accurately, the negative of the time derivative of the flux. The magnitude of the emf is maximum when the flux-time graph is steepest. ΔΦ is the change of the flux in time interval Δt.
As the graph consists of linear segments, the emf is constant within one segment. The vertical lines do not mean anything.
ehild

 

[azizlwl]

Actually there's no maximum or minimum value. Just polarity change due to changes in gradient.Normally verticall line is dotted.

 

[alv]

Thanks heaps for this.

 

[Nickie]

Dear teacher,

Thank you for reaching out for help with this problem. It is understandable that you may be having difficulty understanding the relationship between EMF and change in flux based on the given graphs. Let's break down the concepts to gain a better understanding.

Firstly, EMF stands for electromotive force, which is the voltage generated in a conductor when it is exposed to a changing magnetic field. This means that a change in magnetic flux, which is the amount of magnetic field passing through a given area, will result in an induced EMF.

Now, looking at the graphs, we can see that the change in magnetic flux is increasing or decreasing over time. This means that the magnetic field passing through the conductor is also changing, resulting in an induced EMF. The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux, which is why we see the EMF at its maximum when the change in flux is at its highest point.

To better understand this concept, imagine a simple scenario where a magnet is moving closer to a coil of wire. As the magnet moves closer, the magnetic flux passing through the coil increases, resulting in an induced EMF. As the magnet continues to move closer, the change in flux decreases and the induced EMF decreases as well. Once the magnet is stationary, the change in flux is zero and therefore there is no induced EMF.

In summary, the reason why the induced EMF is at its maximum even while the change in flux is increasing or decreasing is because the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux. I hope this explanation helps clarify the concept for you. If you have any further questions, please feel free to reach out for more assistance. Best of luck with your studies!

Sincerely,