100% going to be starting every answer to any Faraday question with this
But thanks What we're meant to know I'm not sure (hence me asking the question hahaha), graphs like this I just force into my memory
Swag's got you covered, it's definitely Faraday, my favourite Physics hoe
Faraday's Law goes like this:
In words, the induced EMF/voltage is given by the rate of change of magnetic flux with respect to time (there are more complex versions of this formula out there, but this is the principle).
Note that electromotive force (EMF) is interchangeable with the term "voltage" at this level, they are really one in the same. So, the voltage we generate is given by how quickly we are changing the magnetic field. The fact that the negative sign is there reflects Lenz's Law, the induced voltage should OPPOSE the changing field that created it, so essentially:
The two cancel each other out (as we'd expect), if they didn't that would violate Lenz's Law.
Anyway, in terms of the question, the formula itself is enough to answer mathematically. A sine curve is shown, so the negative derivative is a negative cosine curve, answer D. However, a Physics student isn't expected to know how to do this, so let's do it the longer way.
The rate of change of the magnetic field can be considered properly by taking the derivative of the sine curve, or just simply notice that the EMF should be at a peak when the magnetic field is changing rapidly, and when the magnetic field is at a peak (not changing), the induced EMF should be zero. Remember we only have induced EMF when magnetic flux is changing. That eliminates options A and C, because they don't have peaks/troughs in the correct places. We want either B or D.
Now, the next one is where we bring in Faraday's Law for ease of use. The negative sign makes selecting D easier to see. However, Faraday's Law isn't explicitly in the syllabus in the mathematical form, so instead, you could use a Lenz's Law explanation. The EMF
must be opposite in sign to the rate of change of magnetic field, because the induced EMF must oppose the change that created it. So, as the rate of change of magnetic flux is positive (EG - at the start of the top graph), we expect a negative peak (trough) for the EMF. D matches this response
Does this make sense? Definitely a tough question this one, a
tad beyond the syllabus IMO, but definitely within realms of reason, where did you find it?