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Current time:0:00Total duration:9:30

Video transcript

so we have something interesting going on I have this ring of conductor right here the square ring it has a resistance of 2 ohms we see that it is 2 meters by 2 meters so the area of this ring would be 4 square meters and we see a magnetic field going through the surface defined by the ring and it's constant it's a constant magnetic field of five Tesla's it's going exactly perpendicular ly to perpendicularly to the surface of the Ring now what we're going to happen what we're going to see happen is over the next 4 seconds and this is going to happen at a linear rate it's going to happen at a constant rate we're going to see the magnetic field over 4 seconds go from five Tesla's to 10 Tesla so it's going to double over those 4 seconds and by doing so we're going to have a change in flux let's think about what the change in flux is over this 4 seconds so our initial flux let me write it over here so flux we're just a different color and at any time if you are so inspired I encourage you to pause the video and figure out what our change in flux is so our flux flux initial is going to be well it's the it's going to be the constant magnetic field you could say the average magnetic field over the surface but since it's constant that's just going to be five Tesla's so five Tesla's and it helps for it helps us in this problem that the magnetic field vectors are exactly perpendicular to the surface to the surface defined by the ring if they weren't we would have to find the component that is perpendicular but we have that right over there so we have five Tesla's that's the average magnetic field or the average component of the magnetic field that is perpendicular to the surface so five Tesla's times the area of the surface so times well 2 meters times 2 meters is 4 square meters so that is going to be equal to and that is equal to 20 Tesla meter squared Tesla meters squared fair enough now what's the final what's the final flux the final flux flux final is going to be equal to well now now the average magnetic field or the the average components of the magnet field that are perpendicular in the way I've defined this magnetic field the vectors are already perpendicular is 10 Tesla's to 10 Tesla's the area of our of our ring hasn't changed so still four square meters so times four square meters and so what is this going to be so our time our final flux is going to be final flux is going to be forty forty Tesla meters squared so what is our what is our change in flux let me write this over here our change in flux change in flux which is going to be our final flux minus our initial flux is going to be forty Tesla meter squared minus 20 Tesla meter squared which is just going to be 20 Tesla meter squared so we figured out the change in flux we actually know the change in time it's going to be four seconds and actually using that we can now figure out what the voltage induced is going to be the voltage induced to which or the voltage that's going to now induce induce a current and if you look up Faraday's law on the internet you look up for a formula for Faraday's law you would see something that looks like this UT voltage generated is equal to negative and at least if you're not using the calculus version of it negative n times our change in flux change in write change in flux and that just flux change in flux Delta flux over change in time so one way to think about this and to do this problem right we're assuming we have the constant or the rate of change is constant in our flux so you have the average rate of change of your flux and then you're going to multiply it times n n is actually the number of loops you have or you can think of it the number of surfaces defined by it in this exact example in this exact example n is just going to be one we just have one loop so that simplifies it right over there and then so this is going to be and you might say what is this negative because it's a bit of a strange thing because you know how are we defining direction you know what didn't it and all of that and that's why I'm a little bit I'm not a huge fan of this negative sign this is you know if you look it up on in a textbook they'll often say and you're not using calculus they'll say oh this reminder to use lenses law they'll write literally lenses law when I would say if they want a reminder to use lenses law why don't they just remind you to use lenses law instead of putting a a kind of bizarre negative sign there and the negative sign actually does make sense if you're if you were doing kind of the the using the vectors here and and taking the and and using a little bit of the well doing more sophisticated mathematics but this is just saying that the voltage induced is going to be in a direction so to induce a current who's who's induced magnetic field will go in the direction will will counteract the change in flux so that's just lenses law there so the real key here is at least for this example is to find our change in flux over change in time our average or average rate of change in flux and what is this going to be well this is going to be twenty Tesla meters squared twenty Tesla meters squared that was our change in flux right over there divided by our change in time which is four seconds over four seconds which is going to be equal to and I could throw that negative there if we want to that negative 20 divided by four is five five Tesla meter squared square meters per second and this actually turns out to be a volt so we could say this is negative five volts negative negative five volts negative five volts so if you have a voltage of well let's just say five volts we can think about the negative later if you have a voltage of five volts across a car across a circuit that has a resistance of two ohms what is the current and what is the current going to be but we just have to remind ourselves V is equal to I R or voltage is equal to the current divided by the voltage is equal to the current times the resistance or you could say that the current the current is equal to the voltage divided by the resistance so in this case the current the current induced is going to be the voltage and I'm just going to focus on its absolute value now we can think about its direction in a second it's going to be its voltage five volts divided by the resistance so two ohms two ohms which is going to be equal to this is going to be equal to two point five two point five amperes two point five amperes so we now know the magnitude of the current that's going to be induced while we have this change in flux remember this is going to happen while over the course of this four seconds as we have this rate of change of flux this average rate of change of flux which we'll assume is the actual rate of change of flux we're assuming that we it's it's changing at a constant rate and so while it is changing we were just able to figure out that it would induce a current of two point five amperes now the next question we should ask ourselves and this is where this little negative comes in is a reminder for us to use lens's laws well which direction is that current going to go in is it going to go in let me pick two orientations is it going to go in a is it going to go in a in a clockwise direction is it going to go that way over the course of this change in flux or it's going to go into a counterclockwise direction is it going to go that way and to think about that we just have to use the right hand rule take our right hand point our thumb in the direction of the the proposed direction of the current and so if we went with this one our right hand our right hand would look like this I'm literally taking my left hand out and I'm a high right hand out and I'm drawing it and I'm looking at it to think about what would happen so that's my right hand so if I use the right hand rule if the current went in this direction then it would induce a magnetic field that went that went like this and so if the current went in this direction the magnetic field it induces inside the surface would only reinforce the change in flux so it would only add to the flux so and it's going in the same direction as the change in flux which would just keep us you know as we talked about it if you in the Lenz's law video that would turn into justice the source of energy that comes out of nowhere and defies the law of conservation of energy so this absolutely not is not going to be the direction and so we know that the direction is going to be in a clockwise one so the current the 2 point 5 ampere current is going to flow is going to flow like that and we're done by thinking about our change in flux and how long it's taking us we were able to figure out not only the magnitude of the current we're able to figure out the orientation of the direction that is actually going to flow in