EMF and flux explained

I want to explain basically the concept of flux and how changing flux can lead to an EMF in essence what I'm going to be talking about briefly is about Faraday's law but first, let me start to start talking about flux one of those things that students struggle to understand in terms of Faraday's law is the whole nature of flux and one of the ways I try to describe flux in my classroom is to imagine rain falling and the rain represents the magnetic field lines 

    and then I have a loop like this and I hold it up in the rain and I then ask the question how much what water is going to go through my loop well it's pretty clear that there are two factors that determine how much water will flow through my loop first of all how strong is the rain how heavy is the rain how bigger the droplets and how closely are less spaced and the second aspect of that is of course is how big is my loop what's the area and both contribute to how much rain or would capture through the space of my loop the rain represents the magnetic field strength or the magnetic flux density 

    so the heavier rain represents a stronger magnetic field strength or a stronger like magnetic flux density and the area is obviously s as well so the magnetic flux is a measurement really of how much rain I capture or how many magnetic fields lines I capture within my loop and the two factors basically both contribute the density of the lines and the area and as a result, flux is a product of magnetic flux density and mag 

    and the area that is in there now if I turn by a loop in that particular angle there then the area in terms of the ability to capture raindrops to zero and so in In this case, my flux is zero if I were to hold it at a small angle such as this in the area from above is certainly larger than zero but it's smaller than the max an area that I have here again the amount of Reiner will capture the following my analogy will be determined by the smaller area which is certainly a trigonometric ratio reduction of the inner maximum area that 

    I already have so that in essence is magnetic flux so how does an in a changing flux determine the actual EMF that's generated so if I were to start from this particular position you could understand that if I were to rotate this around then my flux would start at zero in this particular point it would crucifix as a maximum as a graph behind me demonstrates and then as I continue around and move in a circle then I would get a sinusoidal curve starting at zero reaching to a maximum and back to zero and then a maximum in the negative direction and as a result that in essence is changed is basically the value of the flux the Faraday's law says actually, 

    EMF is proportional to the rate of change of flux so in this particular position although the flux is actually at zero the change of flux is actually at a maximum, there's a rapid change from zero flux to some sort of positive flux and so at this particular position in the rotation the change of flux is at a maximum whereas in this particular position the change of flux is actually at a minimum even though the flux is actually large the change of flux is actually very small anyway they continue on of course 

    I get as the same sinusoidal pattern but as you can see the actual sine curve or the the curve is actually 90 degrees out of phase the previous one simply because the second curve is a derivative of the first curve but finally of course Faraday said that the EMF is equal to the negative rate of change of flux the negative is due to them as law and so the third graph shows that although he my flux is zero my rate of change lakhs is maximum because of lenses law 

    the EMF is in the negative direction at that particular point as I moved into this position the EMF is obviously zero because the rate of change of flux is zero and then back in this position even though my actual iam flux is zero my rate of change of flux is a negative value but my EMS is a negative value and hence the third graph is there I hope you understand therefore as I turn this I am actually as a result producing an alternating card as the EMF changes every 180 degrees I hope that makes sense Thanks

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