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Faraday's Law - Lenz's Law
PhD., University of Maryland
Jonathan is a published author and recently completed a book on physics and applied mathematics.
The Faraday - Lenz law states that when you have change in magnetic flux, you generate electromotive force. The formula to determine the Faraday - Lenz law is magnetic flux = magnetic field x area.
So let's talk about the Faraday - Lenz law, the Faraday - Lenz law is a very very very important law of our electromagnetic fields that came out of two Physicists Faraday and Lenz and that's why it's called that law. Alright, what it says is that when you have change in magnetic flux you'll generate electromotive force emf and you can think of emf just like voltage it's not exactly the same thing but for all intents and purposes it kind of is.
Alright, so what's magnetic flux? Magnetic flux is magnetic field times the area alright so it consists of two different pieces; how big is the magnetic field and how big is the area over which the magnetic field is acting. Alright, so the way that it works is when I have a change in magnetic flux I generate an electromotive force to run a current around. Now remember that when you've got a current you generate a magnetic field. Now the way that the law works is that systems do not like change so whenever the magnetic flux changes, the current is induced in such a direction as to minimize that change alright that it looks mathematically is emf, emf always looks like an electrified e, equals minus change in magnetic flux divided by change in time, this minus sign is Lenz's law. Lenz said that the magnetic flux change will sorry that the electromotive force will oppose the change in magnetic flux so he gave the minus sign this is Faraday so Faraday - Lenz.
Alright so let's do an example, supposed that I got this situation the magnetic field is directed out of the board and let's say that B decreases alright? So it's out of the board but it's getting smaller. Now remember the way that this works, systems don't like change it's not about trying to make the magnetic field zero it doesn't like change so it had all this magnetic flux already and now the flux is going away so the current is going to try to bring back the flux and it's going to go it's going to generate a current in such a direction that the magnetic field generated from the current is out of the board so it's going to generate a current in that direction if the magnetic field goes down.
Alright, what if the magnetic fields coming out of the board started to increase? Well now we got more magnetic flux but I don't want change so now the current is going to go in the other direction so that the magnetic field opposes that increase in magnetic flux and so that's the way it goes, it's just kind of alright what was the change? And then let's try to mitigate that let's try to make it as small as possible.
Alright now there's one very very very classy example of this and I'm going to show you a YouTube video that illustrates what happens. Now as you watch this happen, the demonstrator is going to drop a magnet down these two sides; this is glass that's aluminum. Notice that the magnet running down the glass landed way before the aluminum did so that's the idea this magnet was coming down, we had a change in magnetic flux because the magnet was moving and then that generated a current in the aluminum that opposed that change it tried to slow the magnet down so that the change was not as big as it would have been otherwise. Now what's interesting about this is that aluminum is not a magnetic material you can take a magnet touch it to alumina it doesn't it doesn't care it's not a magnetic material. This was not a magnetic affect directly it was the current that generated there and even though aluminum it's not a magnetic material it's certainly is a conductor and it will definitely support a current so that's a very very interesting example of how the Faraday-Lenz law works.
Another important example is the use of rail systems like the bart or like the metro in DC the way that these things work is the car is going and then there it goes it goes it goes we get to the station and suddenly there's a magnetic field introduced it doesn't like the change so it tries to stop to make that change take place slower.
Alright let's do an example so this is a numerical example I've got a 5 Tesla magnetic field and it's directed out of the page and it changes to 0 Tesla in 0.1 seconds and I want to know the emf that's generated in a wire loop that has 2 square meters of area and I want to know the average current if the resistance is 20 ohms. Alright so let's see how this goes, first thing I need to do because the emf is equal to minus the change in flux over the change in time I need to find out the change in flux. Well the area of the loop didn't change so it's not the area that changed it's the magnetic field so the change in flux is going to be the change in magnetic field times the area. Well the magnetic field changed from 5 to 0 so the change was -5 times the area which is 2 so we'll have -10 and then it will be Tesla square meters alright, so that is my change in magnetic flux what about the change in time? Well the change in time is 0.1 seconds so the emf will be equal to minus and I've got -10 Tesla meters squared over 0.1 seconds and so that's going to give me 100 and what do you think the unit is? Well we can work through what is the Tesla meters squared per second or we could say it's emf so it must be volts alright everything is in S.I units so everything is in S.I units very very very simple. Alright now I want to know the average current, well if I've got the emf of 100 volts resistance of 20 ohms, current equals v over r so the current will be 5 amps. Now what direction will that current be in? Well if this is my wire, and I've got magnetic field coming out of the board but it's going down right? Then I want to bring back the flux so this is going to be a counter clockwise current.
Alright, now another wonderful example of the use of the Faraday - Lenz law is in the construction of something called a rail gun. What a rail gun is it's a construction like this we've got a wire that comes down I put a little resistor in there wire then comes down like this and then we have here a movable metal bar and this is the rail alright? And then we impose an extremely strong magnetic field on the whole configuration and the more we want to fire it, what do we do? Get rid of the magnetic field very quickly no magnetic field so now what does this system want to do? Well it wants to bring back the flux look there was all that flux it wants to bring it back so it's going to generate a current in this in the direction that will generate a magnetic field into the page so that's like that so this current is going to be going around like that after I turn off the, while I'm turning off the magnetic field. Now notice what happens, I've got a current going down in a magnetic field directed into the page so now I've got a force out like that and this rail is going to accelerate very very very quickly and just be fired off the edge of it and that's a rail gun. Now one interesting way that we can think about this effect instead of thinking about the current, and the force on that, we could change our view point and we could say alright, how can this system act to lower this change in flux? How can it bring back the flux? Well one way that you could do it, it doesn't have as much flux this thing is movable flux is magnetic field times area. Moving this can't change the magnetic field but it can certainly change the area so if I want the flux to remain the same, what I'm I going to do? Well I'm going to increase the area so that B times A won't go down as fast as it would have if I just had the same area and so that's a rail gun and that's the Faraday - Lenz law.
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