Anderson Video - Magnetic Field from a Long Wire

Professor Anderson
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I heard this comedian the other day: "This just in the guy that coined the phrase it's all good has changed his mind. It's not all good. In fact, some is downright horrible that's I thought that was kind of funny. All right. Maybe this is why I made the sidekick, right? It's just a little rim shot. Yeah, there we go. Okay. We've been talking about magnetism, of course. This is a half of electromagnetism. We spent the first few chapters talking about the electric portion of it. Charges make electric fields; these charges in fields feel forces. And now, we're talking about the second half which is magnetism. And in the ensuing chapters, we're actually going to combine the two into one concept -- electromagnetism. So, let's go back to the idea of a current-carrying wire. Okay. So, we're gonna take a long wire and we're gonna give it some current, I. In this wire, there are charges that are moving. Okay? And those charges that are moving, in fact, create a B field. So, a current carrying wire creates a magnetic field. Remember, we use B for a magnetic field. And so, the current creates a B field. Now, the question is: what direction is that magnetic field? If I am sitting over here or over here, there is a magnetic field that is either into the screen or out of the screen. Okay? And, we know what the strength is. We know that the strength is mu naught times I divided by 2 pi r. Where this is, of course, r. How far away are you from the wire? And, mu naught is our good old permeability of free space, and it has a value: 4 pi times 10 to the minus 7. And remember, it has these interesting units on it. It is tesla meter per amp. So, that's the strength of the B field. But now, we need to figure out the direction of the B field. Okay? How do we determine the direction of the B field? Anybody remember? I know. We talked about it all of yesterday ago. It just seems like a long time ago, especially since we had a midterm yesterday. We use something called the right hand rule. Okay? And the right hand rule has several different incarnations and sometimes the books teach it slightly different than I might teach it. Okay? So, you should just practice with the right hand rule to get used to the different approaches. You should end up with the same result. The way you determine the direction is the following: you put your thumb in the direction of the current. And, your curled fingers will then indicate the direction of the B field. Okay? The right hand rule. So, when we're looking at this picture right here and I'm thinking about if I want to put a dot or an X in either of these circles, what should I do on this one right here? Should I put a dot there or should I put an X? What do you guys think? Let's try it. Hold up your right hand. Okay? And remember, when you're looking at me here through the glass in my live studio audience, it's going to get a little confusing. So, don't look at me. Look at the monitor over there. Okay? Hold up your right hand and put your thumb in the direction of the current. Okay? And with your thumb in the direction of the current, your fingers are gonna wrap around in the direction of the B field So, on this side right here, should I put a dot or an X? I should put a dot. Right? Because it's coming out towards you. Remember, dot means out of the screen. Did everybody get that? Did everybody get something coming out of the screen towards them? Okay? You can see the tips of my fingers. Those are coming towards you and so it's out of the screen. Now, by process of elimination, if that is right then this has to be right. On this side, it is into the screen. Okay? And this is why you have to look at the monitor, not at me, because it gets a little confusing because I'm actually using my left hand, right -- to do it up here? And then when we flip it, then it looks like my right hand to everybody at home and watching the computer monitor over here. So, you might think that: "Gee, Dr. Anderson is incredibly ambidextrous and very talented." But, the real answer is we did it a whole bunch yesterday and made a ton of mistakes. Okay? That's -- that's the real answer. Okay. So, if this is the magnetic field of a wire, then it makes circles. Okay? So if I think about drawing a magnetic field loop, it looks like that. And anywhere on this circle you can draw B given by the direction I of the current. B, at this distance away, has a magnitude mu naught I over 2 pi R. So as you go further away from the wire, like you would expect, B gets weaker. Right? There's R in the denominator. And so, it gets weaker. Now, this is also assuming an infinitely thin wire because if R goes to 0 -- if you come back to being on top of the wire -- then this whole thing blows up to infinity. And that's a problem. We don't like infinities in physics. Okay? But, we know that something else is going on once you get to the wire. A real wire is not infinitely thin. It's made up of atoms and molecules. Okay? And so, once you get into there, it becomes a little bit more complicated.
I heard this comedian the other day: "This just in the guy that coined the phrase it's all good has changed his mind. It's not all good. In fact, some is downright horrible that's I thought that was kind of funny. All right. Maybe this is why I made the sidekick, right? It's just a little rim shot. Yeah, there we go. Okay. We've been talking about magnetism, of course. This is a half of electromagnetism. We spent the first few chapters talking about the electric portion of it. Charges make electric fields; these charges in fields feel forces. And now, we're talking about the second half which is magnetism. And in the ensuing chapters, we're actually going to combine the two into one concept -- electromagnetism. So, let's go back to the idea of a current-carrying wire. Okay. So, we're gonna take a long wire and we're gonna give it some current, I. In this wire, there are charges that are moving. Okay? And those charges that are moving, in fact, create a B field. So, a current carrying wire creates a magnetic field. Remember, we use B for a magnetic field. And so, the current creates a B field. Now, the question is: what direction is that magnetic field? If I am sitting over here or over here, there is a magnetic field that is either into the screen or out of the screen. Okay? And, we know what the strength is. We know that the strength is mu naught times I divided by 2 pi r. Where this is, of course, r. How far away are you from the wire? And, mu naught is our good old permeability of free space, and it has a value: 4 pi times 10 to the minus 7. And remember, it has these interesting units on it. It is tesla meter per amp. So, that's the strength of the B field. But now, we need to figure out the direction of the B field. Okay? How do we determine the direction of the B field? Anybody remember? I know. We talked about it all of yesterday ago. It just seems like a long time ago, especially since we had a midterm yesterday. We use something called the right hand rule. Okay? And the right hand rule has several different incarnations and sometimes the books teach it slightly different than I might teach it. Okay? So, you should just practice with the right hand rule to get used to the different approaches. You should end up with the same result. The way you determine the direction is the following: you put your thumb in the direction of the current. And, your curled fingers will then indicate the direction of the B field. Okay? The right hand rule. So, when we're looking at this picture right here and I'm thinking about if I want to put a dot or an X in either of these circles, what should I do on this one right here? Should I put a dot there or should I put an X? What do you guys think? Let's try it. Hold up your right hand. Okay? And remember, when you're looking at me here through the glass in my live studio audience, it's going to get a little confusing. So, don't look at me. Look at the monitor over there. Okay? Hold up your right hand and put your thumb in the direction of the current. Okay? And with your thumb in the direction of the current, your fingers are gonna wrap around in the direction of the B field So, on this side right here, should I put a dot or an X? I should put a dot. Right? Because it's coming out towards you. Remember, dot means out of the screen. Did everybody get that? Did everybody get something coming out of the screen towards them? Okay? You can see the tips of my fingers. Those are coming towards you and so it's out of the screen. Now, by process of elimination, if that is right then this has to be right. On this side, it is into the screen. Okay? And this is why you have to look at the monitor, not at me, because it gets a little confusing because I'm actually using my left hand, right -- to do it up here? And then when we flip it, then it looks like my right hand to everybody at home and watching the computer monitor over here. So, you might think that: "Gee, Dr. Anderson is incredibly ambidextrous and very talented." But, the real answer is we did it a whole bunch yesterday and made a ton of mistakes. Okay? That's -- that's the real answer. Okay. So, if this is the magnetic field of a wire, then it makes circles. Okay? So if I think about drawing a magnetic field loop, it looks like that. And anywhere on this circle you can draw B given by the direction I of the current. B, at this distance away, has a magnitude mu naught I over 2 pi R. So as you go further away from the wire, like you would expect, B gets weaker. Right? There's R in the denominator. And so, it gets weaker. Now, this is also assuming an infinitely thin wire because if R goes to 0 -- if you come back to being on top of the wire -- then this whole thing blows up to infinity. And that's a problem. We don't like infinities in physics. Okay? But, we know that something else is going on once you get to the wire. A real wire is not infinitely thin. It's made up of atoms and molecules. Okay? And so, once you get into there, it becomes a little bit more complicated.