Learn about Magnetism 12: Induced Current in a Wire Video

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Learn about Magnetism 12: Induced Current in a Wire

Let's say I have a magnetic field popping out of this video. So this little brown circles shows us the tips of the vectors popping out of our screen. And then in that magnetic field, I have this wire, off white colored wire. And sitting on that off white colored wire, I have a charged of charge Q. let me write down the other stuff. So this is the magnetic field B, coming out. And let's say I were to take this whole wire. And let's say that the wire overlaps with the magnetic field a distance of L. so let's say the magnetic field stops here. And stops here. And let's say that this distance right here, that distance is L. I drew a little bit weird, but you get the idea. From here to here is L. I have this charged sitting on this some type of conductor that we can consider a wire. And the magnetic field is pushing out of the page. So in this current formation, let's say I don’t have any voltage across this wire or anything, what's going to happen? Well if I just have a stationary charge sitting in a magnetic field, nothing really is going to happen. Right. Because we know that the force due to a magnetic field is equal to charge times the cross product of the velocity of the charge and the magnetic field. If this wire is just stationary, there's no voltage across it, the velocity of this charge is going to be 0. So the velocity is 0, we know that you know, the magnitude of a cross product is the same thing as. So Q, that’s a scalar quantity, so that’s just Q, times the magnitude of the velocity times the magnitude of B times sine theta. And in these situations where, anything that’s going on on this plane is going to be perpendicular to this magnetic field, so the angle between the magnetic field and any velocities that were any within this plane would be 90 degrees. And you wouldn’t have to worry about sine theta too much. But we see, if the velocity is 0 or the speed is 0, the magnitude of the velocity is 0. That there's not going to be any net force due to the magnetic field on this charge. And nothing interesting is going to happen. But let's do a little experiment. What happens if I were to move this wire? If I were to shift it to the left with the velocity V. So I take this wire and I shift it to the left with the velocity V. So the whole wire is shifting to the left. Well the whole wire is shifting to the left, this charge is sitting on that wire. Right. So that charge is also going to move to the left with the velocity V. And now things get interesting. The charge is moving to the left with a velocity V. So now we can apply the first magnetism formula that we learned. We can apply this formula. So what's going to happen to this charge? Well the force of the charge is going to be the charge times the magnitude of the velocity cross the magnetic field vector. So we know that there's going to be some net force, this is non-zero now. And this is non-zero, were assuming. And we’re assuming the charge is non-zero. So what direction is the force going to be in? So let's do our right hand rule from the cross product. V cross B will give us the direction. So point your index finger in the direction of the velocity. And I have to look at my own hand to make sure I'm doing it right. So you point your index finger in the direction of the velocity. Point your middle finger in the direction of the magnetic field. The magnetic field is popping out of the page. So your middle finger is actually going to be popping out of the page. Your next two fingers are going to do something like that. So you're kind of approximating like you're shooting a gun. Then what's your thumb going to do? Your thumb is going to point straight up. So this is your palm, that’s your thumb. This could be your nail, fingernail of your thumb. Fingernail of your middle finger. Right, these are the direction of the velocity. The velocity is that way. The magnetic field is popping out of the page. So, the force on the particle, on this charged particle due to the magnetic field is going to go in the direction of your thumb. So the direction of the force is in this direction. So the force. So what's going to happen? There's going to be a net force in this direction on the charge. And the charge is going to move upwards. Right. When you're starting to move, you can imagine all of a sudden that you have a multiple charge right. If you had multiple charges here and you're moving the whole wire, all of those charges will going to be moving upwards. And what is another way to call a bunch of moving charges along a conductor? Well, it’s a current. Depending on how much charge is moving per second. So at least in a very qualitative terms, your C. That when you move a wire through a magnetic field or when you move a magnetic field pass a wire, right. Because they're kind of the same thing. It’s all about the relative motion. But if you move a wire through a magnetic field is actually going to induce a current in the wire. And it’s going to induce current in the wire and actually this is how electric generators work. And I’ll do a whole series of videos on if you’re using coal or steam or hydro power, how that turns these generators around and induces current. That’s how we get electricity from all of these various energy sources. That essentially make turbines turn. But anyway, let's go back to what we were doing. So, let me ask you a question, if this particle and this all has a point, if this particle starts in the beginning. Let's say the particle is right here, so it starts right where the magnetic field start affecting the wire, how much work is going to be done on the particle by the magnetic field? Well, what's work, work is equal to force times distance. But the force has to be in the same direction as the distance. I won't mess with the vectors right now. But they have to be in the same direction. So how much work is going to be done on this particle? So the work is going to be the net force exerted on the particle times the distance. Well this distance is L, once the particle gets here, there's no magnetic field up here. So the magnetic field will stop acting on it. So the total work done, work, which is equal to force times distance. It’s equal to, so the net force is this up here, Q, I’ll leave some space, V cross B times the distance. So the distance right here is just a scalar quantity so we could put it off front. Right, Q times L times V cross B. Right. This is Q, V cross B, its force times the distance. That’s just the work done. Now, how much work is being done per charged? Right. This is how much work being done on this charge, but let's say there might have been multiple charges. We just want to know how much work is done per charge. So work per charge, we could divide both sides by charge. So work per charge is equal to this per charge. So it is equal to the distance times the velocity that you're pulling the wire to the left with, cross the magnetic field. This is where it gets interesting. So what is work per charge? The units of work are energy, right. Joules. And charge, that’s in coulombs. So what are joules per coulomb? This is equal to volts. Volts are joules per coulomb. So these charges are going to start moving in this direction as if there is a voltage difference, as if there is a potential difference between this point and this point. As if this is a positive voltage and this is a minus voltage. So there is actually going to be a voltage or perceive voltage difference between this point and this point that will start making the current flow. Let's say you didn’t even know that there was a magnetic field in here. You would just see this current flow and you're like, oh, well there has to be a voltage difference. Right. But when we’re dealing with this, because we talked about voltages, that was like a potential difference. That a particle or charge has a higher potential energy and that’s why it’s moving. But it’s hard to, at least for this purposes to say, well you have a higher potential energy here. It’s really being created by the magnetic field. So in this context, people have said, that instead of saying that this is creating a voltage difference between this point and this point. That the magnetic field on the moving wire is causing that, people say that it’s creating an electro motive force, or EMF. But EMF, the units are still joules per coulomb or volts. And it really is, in every way, we are analyzing the circuit, still the same thing as a potential difference or as a voltage difference. But since it seems a little bit more proactive, it seems like this magnetic field is actually impacting a force on this wire that causing the current to move, we call it EMF. Right. So we could say that the EMF, the Electro Motive Force, or the voltage across from here to here. They really the same thing, is equal to the distance of the wire that’s in the magnetic field times the velocity that you're pulling the wire in cross the magnetic field. So let's say, I don’t know, let's just throw in a bunch of numbers. Let's say that the magnetic field, I’ll make is easy, 2 teslas. My velocity to the left is 3 meters per second. And let's just for fun, let's give this a little bit of a resistance so we can figure out something. So let's say this resistance is 6 ohms. There's a 6 ohm resistance here. So the resistance of the wire from here to here is 6 ohms. All wires have some resistance to it. So first of all, what's the EMF? And let's say that this total distance right here is 12 meters. So the EMF or the electro motive force put on to the wire by the magnetic field is going to equal the distance of the wire in the magnetic field, 12 meters. Times, well, were just taking the cross product, we know that the velocity is perpendicular to the magnetic field. So we don’t have to worry about sign theta, because theta is already 90 degrees. So we just have to worry about the magnitudes. So it’s going to be 12 meters times the velocity, which is 3 meters per second, times the magnetic field or the magnitude of the magnetic field, that’s 2 teslas. And so the EMF is 12 times 3 times 2, which is 72 volts or 72 joules per coulomb. And now you have that potential difference, that EMF, across a 6 ohm resistor. Right. So that, you just go back to voltage is equal to IR or you could write EMF is equal to IR. So EMF divided by resistance. So if we take this EMF and we divide it by the resistance, divided by 6 ohms. We got the current, right. EMF divided by resistance is equal to current. So you divide 72 volts or 72 joules per coulomb divided by 6 ohms. And then you get current going along this wire right here, due to the EMF, due to the magnetic field. I know it’s very messy at this point of 12 amperes. Anyway, I'm all out of time. I’ll see you in the next video.

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Let's say I have a magnetic field popping out of this video. So this little brown circles shows us the tips of the vectors popping out of our screen. And then in that magnetic field, I have this wire, off white colored wire. And sitting on that off white colored wire, I have a charged of charge Q. let me write down the other stuff.
So this is the magnetic field B, coming out. And let's say I were to take this whole wire. And let's say that the wire overlaps with the magnetic field a distance of L. so let's say the magnetic field stops here. And stops here. And let's say that this distance right here, that distance is L. I drew a little bit weird, but you get the idea. From here to here is L. I have this charged sitting on this some type of conductor that we can consider a wire. And the magnetic field is pushing out of the page.
So in this current formation, let's say I don’t have any voltage across this wire or anything, what's going to happen? Well if I just have a stationary charge sitting in a magnetic field, nothing really is going to happen. Right. Because we know that the force due to a magnetic field is equal to charge times the cross product of the velocity of the charge and the magnetic field.
If this wire is just stationary, there's no voltage across it, the velocity of this charge is going to be 0. So the velocity is 0, we know that you know, the magnitude of a cross product is the same thing as. So Q, that’s a scalar quantity, so that’s just Q, times the magnitude of the velocity times the magnitude of B times sine theta. And in these situations where, anything that’s going on on this plane is going to be perpendicular to this magnetic field, so the angle between the magnetic field and any velocities that were any within this plane would be 90 degrees. And you wouldn’t have to worry about sine theta too much. But we see, if the velocity is 0 or the speed is 0, the magnitude of the velocity is 0. That there's not going to be any net force due to the magnetic field on this charge. And nothing interesting is going to happen.
But let's do a little experiment. What happens if I were to move this wire? If I were to shift it to the left with the velocity V. So I take this wire and I shift it to the left with the velocity V. So the whole wire is shifting to the left. Well the whole wire is shifting to the left, this charge is sitting on that wire. Right. So that charge is also going to move to the left with the velocity V. And now things get interesting. The charge is moving to the left with a velocity V. So now we can apply the first magnetism formula that we learned. We can apply this formula.
So what's going to happen to this charge? Well the force of the charge is going to be the charge times the magnitude of the velocity cross the magnetic field vector. So we know that there's going to be some net force, this is non-zero now. And this is non-zero, were assuming. And we’re assuming the charge is non-zero. So what direction is the force going to be in?
So let's do our right hand rule from the cross product. V cross B will give us the direction. So point your index finger in the direction of the velocity. And I have to look at my own hand to make sure I'm doing it right. So you point your index finger in the direction of the velocity. Point your middle finger in the direction of the magnetic field. The magnetic field is popping out of the page. So your middle finger is actually going to be popping out of the page. Your next two fingers are going to do something like that. So you're kind of approximating like you're shooting a gun. Then what's your thumb going to do? Your thumb is going to point straight up. So this is your palm, that’s your thumb. This could be your nail, fingernail of your thumb. Fingernail of your middle finger. Right, these are the direction of the velocity. The velocity is that way. The magnetic field is popping out of the page.
So, the force on the particle, on this charged particle due to the magnetic field is going to go in the direction of your thumb. So the direction of the force is in this direction. So the force. So what's going to happen? There's going to be a net force in this direction on the charge. And the charge is going to move upwards. Right. When you're starting to move, you can imagine all of a sudden that you have a multiple charge right. If you had multiple charges here and you're moving the whole wire, all of those charges will going to be moving upwards. And what is another way to call a bunch of moving charges along a conductor? Well, it’s a current. Depending on how much charge is moving per second.
So at least in a very qualitative terms, your C. That when you move a wire through a magnetic field or when you move a magnetic field pass a wire, right. Because they're kind of the same thing. It’s all about the relative motion. But if you move a wire through a magnetic field is actually going to induce a current in the wire. And it’s going to induce current in the wire and actually this is how electric generators work. And I’ll do a whole series of videos on if you’re using coal or steam or hydro power, how that turns these generators around and induces current. That’s how we get electricity from all of these various energy sources. That essentially make turbines turn.
But anyway, let's go back to what we were doing. So, let me ask you a question, if this particle and this all has a point, if this particle starts in the beginning. Let's say the particle is right here, so it starts right where the magnetic field start affecting the wire, how much work is going to be done on the particle by the magnetic field?
Well, what's work, work is equal to force times distance. But the force has to be in the same direction as the distance. I won't mess with the vectors right now. But they have to be in the same direction. So how much work is going to be done on this particle? So the work is going to be the net force exerted on the particle times the distance. Well this distance is L, once the particle gets here, there's no magnetic field up here. So the magnetic field will stop acting on it. So the total work done, work, which is equal to force times distance. It’s equal to, so the net force is this up here, Q, I’ll leave some space, V cross B times the distance. So the distance right here is just a scalar quantity so we could put it off front. Right, Q times L times V cross B. Right. This is Q, V cross B, its force times the distance. That’s just the work done.
Now, how much work is being done per charged? Right. This is how much work being done on this charge, but let's say there might have been multiple charges. We just want to know how much work is done per charge. So work per charge, we could divide both sides by charge. So work per charge is equal to this per charge. So it is equal to the distance times the velocity that you're pulling the wire to the left with, cross the magnetic field.
This is where it gets interesting. So what is work per charge? The units of work are energy, right. Joules. And charge, that’s in coulombs. So what are joules per coulomb? This is equal to volts. Volts are joules per coulomb. So these charges are going to start moving in this direction as if there is a voltage difference, as if there is a potential difference between this point and this point. As if this is a positive voltage and this is a minus voltage. So there is actually going to be a voltage or perceive voltage difference between this point and this point that will start making the current flow. Let's say you didn’t even know that there was a magnetic field in here. You would just see this current flow and you're like, oh, well there has to be a voltage difference. Right. But when we’re dealing with this, because we talked about voltages, that was like a potential difference. That a particle or charge has a higher potential energy and that’s why it’s moving.
But it’s hard to, at least for this purposes to say, well you have a higher potential energy here. It’s really being created by the magnetic field. So in this context, people have said, that instead of saying that this is creating a voltage difference between this point and this point. That the magnetic field on the moving wire is causing that, people say that it’s creating an electro motive force, or EMF. But EMF, the units are still joules per coulomb or volts. And it really is, in every way, we are analyzing the circuit, still the same thing as a potential difference or as a voltage difference. But since it seems a little bit more proactive, it seems like this magnetic field is actually impacting a force on this wire that causing the current to move, we call it EMF. Right. So we could say that the EMF, the Electro Motive Force, or the voltage across from here to here. They really the same thing, is equal to the distance of the wire that’s in the magnetic field times the velocity that you're pulling the wire in cross the magnetic field.
So let's say, I don’t know, let's just throw in a bunch of numbers. Let's say that the magnetic field, I’ll make is easy, 2 teslas. My velocity to the left is 3 meters per second. And let's just for fun, let's give this a little bit of a resistance so we can figure out something. So let's say this resistance is 6 ohms. There's a 6 ohm resistance here. So the resistance of the wire from here to here is 6 ohms. All wires have some resistance to it.
So first of all, what's the EMF? And let's say that this total distance right here is 12 meters. So the EMF or the electro motive force put on to the wire by the magnetic field is going to equal the distance of the wire in the magnetic field, 12 meters. Times, well, were just taking the cross product, we know that the velocity is perpendicular to the magnetic field. So we don’t have to worry about sign theta, because theta is already 90 degrees. So we just have to worry about the magnitudes. So it’s going to be 12 meters times the velocity, which is 3 meters per second, times the magnetic field or the magnitude of the magnetic field, that’s 2 teslas. And so the EMF is 12 times 3 times 2, which is 72 volts or 72 joules per coulomb.
And now you have that potential difference, that EMF, across a 6 ohm resistor. Right. So that, you just go back to voltage is equal to IR or you could write EMF is equal to IR. So EMF divided by resistance. So if we take this EMF and we divide it by the resistance, divided by 6 ohms. We got the current, right. EMF divided by resistance is equal to current. So you divide 72 volts or 72 joules per coulomb divided by 6 ohms. And then you get current going along this wire right here, due to the EMF, due to the magnetic field. I know it’s very messy at this point of 12 amperes.
Anyway, I'm all out of time. I’ll see you in the next video.

Transcription by: Scribe4you Transcription Services