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Current time:0:00Total duration:8:02

Video transcript

so I have an interesting setup over here I have a magnetic field that is constant and it's going straight out of as you say the surface of this loop the magnetic the the magnitude of the magnetic field at any point of the surface is going to be B and what we what's interesting here is this loop that we have this right part of the loop is movable you can imagine it's a cylinder here that can roll to the right and the magnitude of its velocity we're going to say is lowercase V and this this cylinder let's say it has length L so given that you can see that we're going to have a change in magnetic flux Y we're going to have a change in magnetic flux or a change in magnetic flux through the surface well if this thing is moving to the right if this thing is moving to the right when it's speed is V and it could be any units m/s or whatever it is you're going to even though the magnetic field itself is constant you're actually going to be changing the area the area that is I guess you could contained by this loop and so that is going to give us a change in flux and if you have a change in flux that is going to induce an electromagnetic that's going to induce an electro-motive force or it's going to induce a voltage in this loop which will cause a current to flow so let's think about what that electro-motive force that's going to be induced is going to be and I'm just going to rewrite Faraday's law right over here priority's law negative n times our change in our change in flux and we're talking about the the well our change in flux over change in let me write that a little bit neater our change in our change in flux over change in time now the N is the number of loops we're talking about so in this case n is just going to be 1 and the negative I've already complained a little bit about it in previous videos this is really just reminding us the math when you when you're not using kind of proper vector mathematics this just reminds us that this EMF is going to cause a current to go through this loop and the end the magnetic field that is induced by that current will go against the direction of our change in flux so that's that's just something something to remind us there so what we really care about what we really care about is our change in flux over change in time so what is that going to be let me just write it here our change in flux our change in flux over change in time well our change in flux in this case it's going to be our change in our the magnitude of our magnetic field that is going perpendicular to the surface times the area of our surface over our change in time and what is this going to be equal to well B is constant it's not going to change over the time that we care about so the change in B times a it's really just going to be B times our change in area B times our change in area over how much over how much time goes by so what is our change in area going to be so let's say that we let Delta T so let's say Delta T goes happens what is going to be our change in area well let's let Delta t go on so if delta T goes on this this cylinder or if we wait for you know T units of time so R of T units of time go by so let me do this in another color so let me see I have not used let's see so I'm going to use this color right over here so how far will we go after delta T well we know the magnitude of our velocity if you multiply the magnitude of your velocity times your change in time that will give you the Mac that will give you your distance and so your change in area is going to be the amount of distances traveled times the length of the rod times the length of the rod which is just that so our change in area which is that area right over there our change in area our change in area over that time is going to be the distance this rod goes and notice this rod is going in a direction that is perpendicular to the direction of the Magna field that's an important thing to realize and so we have we have our change in area is going to be this chain this dimension which is how far the rod travels times the length of the rod that's how much area we gain that's how much it increases our area increases so x times the length of the rod that's our change in area so then we can substitute that back over here so this is going to be equal to and this is going to be equal to we get our B we have our change in time and our change in area we just said is going to be it's going to be let me just write it this way I could write it as the length of our rod times the magnitude of our velocity or our speed times our change in time well change in time divided by change in time those cancel out so our change in our change in our change in flux over that time or a raid or our average our average rate of change in flux we see simplifies to the length of our rod times the magnitude of our velocity or our speed times the magnitude of the magnetic field that is going perpendicular to the surface and this is something that you will see many times in your in your physics class this whole notion of hey if your rod going in a perpendicular direction to a magnetic field it induces an electro-motive force of lvb well this is where it's coming from it's coming directly from Faraday's law and you could say okay if it's if it's if that's happening what direction is that is the current going to actually flow in well if the the magnetic field isn't changing but since the area is increasing the flux is increasing in the in the upward direction so you could say the flux is increasing in that direction so the current that gets induced and the the magnitude of the current is going to be based on how much resistance we have but the current is going to induce a magnetic field that goes against our change against our change in flux so let's see if the current went if the current went that way if the current goes that way what will happen so I'm going to take my right hand out so if I take my right hand out my thumb in that direction and if I were to loop my fingers around if I were to loop my fingers around this would if the if we went that way this would describe this would induce a magnetic field that goes like this that goes like this so that actually would enhance the flux going through or the change in flux go in the same direction of the change in flux we've already talked about this would violate the the law of conservation of energy so the current is going to go in the other direction the current is going to go in the other direction it's going to go in this case it's going to go clockwise because the current is going to induce a magnify let's again I can take my right hand out and try to draw my right hand and we can see now the direction of my fingers go in are that way and notice we're looking at the inside of the surface so the inside of the surface the surface area was increasing so is increasing the flux in you could say I guess you say the upward direction we're getting more of those more of the magnetic field in the upper direction being contained in the area so the magnetic field induced by the current that is induced which is caught or that current is caused by the electro-motive force and depend the magnitude of current is going to be dependent on our resistance that's going to go in the other direction it's going to go down that way so it's going to induce a magnetic field that is going to go downwards so the current needs to be going clockwise