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So not only can a magnetic field exerts some force on a moving charge, were now going to learn that a moving charge or current can actually create a magnetic field. So there is some type of symmetry here and as will learn later when we learn our calculus and we do this in a slightly more rigorous way. Well see that electro that magnetic field and electric fields are actually two sides of the same coin of really electro magnetic fields but anyway we won’t worry about that now and I think it’s enough to ponder right now that a current can actually induce a magnetic field.
And actually just a moving electron creates a magnetic field and it does it in a kind of a surface of this but I wont go into all of that right now because the math gets a little bit fancy there but what you might encounter in your standard high school physics class is not getting deeply into vector calculus because if you just have a wire. Let me a draw a wire that’s my wire and its carrying some current eye. It’s carrying some current I.
It turns out that this wire will generate a magnetic field and the shape of that magnetic field is going to be concentric circles around this wire. Let me see if I can draw that. So here I'll draw it just like how I do when I try to do rotations of solids in the calculus video. So the magnetic field it would go behind and infront and it goes like that or another way you can think about it is if lets go down here is on the left side of this wire. If you say that the wire is the plane of this video.
The magnetic field is popping out of you screen. It’s popping out of the screen and on this side on the right side. The magnetic field is popping into the screen. It’s going into the screen. All right you could imagine that right. This you can imagine if on this drawing up here. You can say this is where it intersects the screen. All of this is kind of behind the screen and all of this is this infront of the screen and this is where it’s popping out, and this is where it’s popping into the screen.
Hopefully that makes a little bit sense and how did I know that it’s rotating this way? Well it actually does come out of the cross product when you do it with a regular charge and all of that but were not going to into that right now. and so there's a different right hand rule that you can use and its literally you hold this wire or you’ll imagine this holding this wire with your right hand with your thumb going in the direction of the current. And if you hold this wire with your thumb going into the direction of the current, you’re fingers are going to go in the direction of the magnetic field.
So let me see if I can draw that. I will draw it blue. So if this is my thumb, my thumb is going along the top of the wire and then my hand is curling around the wire. All right those are my knuckles; those are the veins on my hand. This is my nail. So as you can see if this was; if I was holding that same wire. Let me draw the wire. So if I was holding that same wire. We see that my thumb is going into the direction of the current. So this is a slightly new thing to memorize and what is the magnetic field doing?
It was going in the direction of my fingers, right. My fingers are popping out on this side of the wire. All right there coming out on this side of the wire and there going in or at least my hand is going on that side. So it’s going into the screen. Hopefully that makes sense. Now how can we qualify? But before we qualify, let’s get a little bit more of the intuition of what's happening. It turns out that the closer you get to the wire. The stronger the magnetic field and the further you get out the weaker the magnetic field. And that kind of make sense if you kind of imagine the magnetic field spreading out. You know well I don’t want to go into to the skin now but if you imagine the magnetic field spreading out as it goes further and further out. It kind of gets distributed over a wider and wider circumference.
And actually the formula I'm going to give you kind of has the taste for that. So the formula for the magnetic field and it really is to find with the cross products and things like that but for our purposes we won’t worry about that. You’ll just have to know kind of if this is the shape. If the current is going in that direction and of course if the current was going downwards. Then the magnetic field would just reverse direction but it will still be in concentric circles around the wire.
But anyway, what is the magnitude of that field? it is the magnitude of that magnetic field is equal to Mu which is a greek letter which I will explain in a second times the current divided by 2phi R. so this has a little bit of a field for what I was saying before that the further you go out where R is how far you are from the wire, right. The further you go out, if R is gets bigger the magnitude of the magnetic field is going to get weaker and this 2phi R that looks a lot like the circumference of a circle.
So that gives you a taste for it. I know I haven’t proved anything rigorously but at least it gives you sense. Oh look there's a little form of the circumference of a circle here and that kind of makes sense right because the magnetic field at that point is kind of a circle. The magnitude is equal and an equal radius around that wire. Now what is this Mu this thing that looks like a U? Well that’s the permeability of the material that the wire is in.
So the magnetic field is actually going to have a different strength depending on whether this wire is going through. Rubber whether it’s going to a vacuum or air or metal or water and for the purposes of your high school physics class. We assume there's going through air normally and the value for air is pretty close to the value for vacuum, and its call the permeability of a vacuum. And I forget what that value is, I could look it up but it actually turns out that your calculator has that value. So let’s do a problem just to put some numbers to the formula.
So let say I have this current and it is I don’t know the current is equal to, I'm going to make a number two amperes. Two amperes and let say that I am that I just pick a point right here that is, let say that’s three meters away from the wire and questions. So my question to you is what is the magnitude into the direction of the magnetic field right there? Well the magnitude is easy. We just substitute in this equation. So the magnitude of the magnetic field at this point is equal to per and we assume that the wire is going through air or vacuum. The permeability of free space that just the constant, all it look fancy times the current times 2 amperes divided by 2phi R. what's R’s? It’s Three meters, so 2phi x 3 = permeability of free spaces. You’ll see the two and the two cancel out over 3phi.
So how do we calculate that? Well we get our trustee TI-85 calculator and I think you’ll be maybe pleasantly surprise or shock to realize that I have to delete everything just so you can see how I get there that it actually has the permeability of free space stored in it. So what you do is you’re going to suck in and you press constant which is the four button. They say the built in constants and let see it’s not one of those. You press more. Its not one of those, press more. Oh look at that, mu not. The permeability of free space that’s what I need and I have to divide it by 3phi, divided by 3 and then where is phi? There it is, its over the power sign, divided by 3phi. It equals 1.3 x 10 to the -7. It’s going to be Teslas.
The magnetic field is going to be equal to 1.3x10 to the -7th Teslas. So it’s a fairly, a fairly weak magnetic field and that’s why you don’t have metal objects being thrown around by the wires behind your television set. But anyway hopefully that’s gives you a little bit and you know—just so you know its not all fits together. So were saying that, these moving charges not only they can be affected by magnetic field. Not only can a current be affected by magnetic field or just a moving charge. It actually creates them and that kind of creates a little bit of symmetry in your head hopefully because if that was also true of electric field.
A charge, a stationary charge is obviously pulled or pushed by a static electric field and it also creates its own static electric field. So it’s always in the back of your mind because if you keep studying physics you’re going to actually prove to yourself that electric and magnetic fields are two sides of the same coin and it just looks like a magnetic field when you’re in a different frame of referent. When something is whizzing pass you, well if you’re whizzing along with it then that thing would look static and then it would might look a little bit more like an electric field.
But anyway I'll leave you there now and in the next video I will show you what happens when we have two wires carrying current parallel to each other, and you might guess that they might actually attract or repel each other. Anyway I'll see you in the next video.