Faraday's Law for generating electricity

we've already looked at Faraday's law in some detail it showed us that if we have some some loop of conductor and we have we have a change in magnetic flux over time through the surface defined by that loop it's going to induce an EMF through that loop which will cause a current to start to to circulate through that loop and that current of course will be dependent on the actual resistance of the conductor and there's many ways that we've already seen of having a change in magnetic flux one you could have a change in the magnetic field you could it could be a change in its magnitude and/or its orientation you can have a change in the shape of the actual loop of conductor if it's area increases or decreases that will change the flux remember the flux is just your the component of the magnetic field that is that is perpendicular to the surface if you take the average of that times the area of the surface and then the other way that we're going to study in this video is inducing an electro mat an electro-motive force by changing it not the shape of the loop and not the magnetic field but by changing the orientation of the loop and in particular we're going to have the loop rotate so let's think about this so I have this loop here it's connected to this axle and I'm going to rotate it in a I'm going to rotate it in a clockwise direction through this mat constant magnetic field you can see it's constant of the magnetic field vectors I've just sampled them at different points in the field they're all pointing straight up and I've drawn them so that they all have the same magnitude now what we need to appreciate is as we rotate this the angle between the magnetic field and the surface is changing and right from this point as we rotate in this clockwise direction the component of the magnetic field that is perpendicular to the surface is going to increase now what am I talking about well let's look at it from this point of view let's look at it from the point of view of the actual loop of wire so from this point of view the magnetic field is at some angle I could draw that angle here so you know whatever angle it's a little hard to see whatever angle this is we could say that is that angle here and as we rotate the entire loop attached to some type of an axle here in a clockwise direction what is going to happen to this angle well after let's say delta T and let's say we're just rotating it a at a constant rate we're going to have the magnetic so after we've rotated a little bit the the magnetic field a vector is going to look something like that so it's the component that is perpendicular to the surface which what we care about for flux it's going to go from being like this it's going to go from being like that to going to being to being like this to being like this so at least for this point of the rotation for this point of the rotation until we get to the flat until we get to the flat point until we have our until we have our loop being completely flat the purpose the the component of our magnetic field that is perpendicular is going to increase which is going to have so we're going to have an increase in flux over that time so if we have an increase in flux over that time as we rotate up at least until we get to the flat point what is going to happen well we're going to induce a current and then we just have to think about what is the orientation of the current so we want to have a current that will induce a magnetic field that will go against the change in flux so the current should induce a magnetic field that is if our flux at least for that part of the rotation is is increasing in the upwards direction if we're from the point of view of of this loop then we need to create a magnetic field that is acting against that so a magnetic field that is acting against that or where you need to create we're going to induce a current that induces a magnetic field that acts against that change in flux so how do I what what type of a current would induce a magnetic field like that so I just use the right hand rule my fingers would go in the direction of these of the of the magnetic field so my fingers and I have to use my right hand so my fingers are going to go in that direction so my right hand my thumb my thumb would go in this direction so that is going to be the direction of the current that is induced so the whole point of me showing you this is that there's multiple ways to have a change in magnetic flux and there's multiple ways to induce a current and this one is particularly interesting because it lets you at low or we can start to think about wow I could turn I could turn a mechanical rotation into an induced current and this is this basic principle although they wouldn't use such a simple loop like this is exactly how electric generators work they're actually in some ways the reverse of an electric motor an electric motor has a current that causes something to rotate here we're having something rotate causing a current to form and that's actually what we have happening when you look at something like windmills or when you look at hydroelectric generators right over here this windmill the wind is going to cause these blades to turn around and then inside inside of this little place right over here you're going to have a more fancy version of this rotating which is going to induce a current and the magnetic field isn't going to be exactly like this and it's going to be a more sophisticated mechanism but it's the same underlying principle it's just Faraday's law at work same thing with hydroelectric generator you're using the potential energy of the flowing water to turn an axle and then that helps us generate electricity by the exact same principle