Pearson+ LogoPearson+ Logo
Start typing, then use the up and down arrows to select an option from the list.

Anderson Video - Electromagnetic Wave Propagation Vector

Professor Anderson
Was this helpful?
<font color="#ffffff">And it says the following: it says an electromagnetic wave is traveling</font> <font color="#ffffff">straight down toward the center of the Earth, at a certain moment in time the</font> <font color="#ffffff">electric field points west. In which direction does the magnetic field point</font> <font color="#ffffff">at this moment? So remember yesterday when we drew electric and magnetic</font> <font color="#ffffff">fields that combine to make a wave, we said the following.</font> <font color="#ffffff">E, let's let that oscillate up and down.</font> <font color="#ffffff">Okay, and we know what that means, it's going up,</font> <font color="#ffffff">then it's going down, up and down and so forth.</font> <font color="#ffffff">But the B field was at a right angle to that.</font> <font color="#ffffff">So if we draw the B field, let's try it in green,</font> <font color="#ffffff">the B field in fact comes into and out of the page.</font> <font color="#ffffff">Okay, so it's pointing out of the page and into the page over</font> <font color="#ffffff">and over again, both of these things are of course oscillating sinusoidally,</font> <font color="#ffffff">and so this would be the direction of B.</font> <font color="#ffffff">Now, the whole wave propagates to the right.</font> <font color="#ffffff">So the wave propagation direction is to the right,</font> <font color="#ffffff">but there is a certain relationship between the E field and the B field.</font> <font color="#ffffff">Okay, and to figure out how to calculate the propagation direction</font> <font color="#ffffff">we can again go back to our right hand rule.</font> <font color="#ffffff">Okay, so the right hand rule is the following:</font> <font color="#ffffff">you put your fingers straight in the direction of E,</font> <font color="#ffffff">you bend your fingers in the direction of B,</font> <font color="#ffffff">and then the propagation direction,</font> <font color="#ffffff">which later on we're going to learn is actually given with a K,</font> <font color="#ffffff">propagation K</font> <font color="#ffffff">is in fact the direction of your thumb.</font> <font color="#ffffff">Okay, so let's try that with this picture and</font> <font color="#ffffff">see if we can convince ourselves that it is true.</font> <font color="#ffffff">And let's look at the first instant of time. In the first</font> <font color="#ffffff">section of this wave, I have an E field that is pointing up.</font> <font color="#ffffff">I have a B field that is coming out of the page and therefore my</font> <font color="#ffffff">thumb gets me the direction of K. So everybody look at the computer monitor,</font> <font color="#ffffff">hold up your right hand, okay, and try that. Put your finger straight up in the</font> <font color="#ffffff">direction of E and now bend your fingers in the direction of B.</font> <font color="#ffffff">Your thumb should be pointing in the direction of K.</font> <font color="#ffffff">Is that what everybody is seeing? No? Okay.</font> <font color="#ffffff">We could have -- we could have it flipped let me see if I can see what's going on in the</font> <font color="#ffffff">computer monitor. So we've got E going up and then B is coming out towards you</font> <font color="#ffffff">guys, is that all right? Okay, and so you should get</font> <font color="#ffffff">a thumb that's going to your right, if you look in the computer monitor.</font> <font color="#ffffff">>> (student speaking) [inaudible]</font> <font color="#ffffff">>> Yeah, don't look at this, this is confusing,</font> <font color="#ffffff">right? Look at that. Is that working over there? Does that look like my right hand</font> <font color="#ffffff">in the computer monitor? Looks like my right hand, right? My fingers are in the</font> <font color="#ffffff">direction of E, yes? Now I'm in the direction of B because it's coming out</font> <font color="#ffffff">towards you and now my thumb is going in the direction of K. Is that working?</font> <font color="#ffffff">Yeah, it gets confusing when you're looking over here at the glass because</font> <font color="#ffffff">it's inverted on the screen and so we have to do a little clever trick there.</font> <font color="#ffffff">So, the relationship between E and B, those two angles determine the direction</font> <font color="#ffffff">of K. E is always orthogonal to B, and if you use your right hand rule, it will</font> <font color="#ffffff">tell you the direction of K. So let's go back to the question that they had for a</font> <font color="#ffffff">second. They said that an electromagnetic wave</font> <font color="#ffffff">is traveling straight down towards the center of the earth at a certain moment</font> <font color="#ffffff">in time, the electric field points west. Okay.</font> <font color="#ffffff">In which direction does the magnetic field point at this moment? All right.</font> <font color="#ffffff">Well, let's see if we can draw this picture, and it might be kind of tricky</font> <font color="#ffffff">to draw but let's give it a shot. This is the Earth, okay, and we're going to say</font> <font color="#ffffff">that the West is to the left, the East is to the right. Okay,</font> <font color="#ffffff">that means the North would be into the screen, South would be out of the screen,</font> <font color="#ffffff">and so if the wave is propagating down towards the center of the earth, it's</font> <font color="#ffffff">going to be coming down this way, and at a certain moment in time the electric</font> <font color="#ffffff">field points West. Okay, so here comes our wave, it is propagating this way and at</font> <font color="#ffffff">this moment in time the electric field is pointing to the West. So there is our</font> <font color="#ffffff">electric field. So if the electric field is pointing West and the wave is</font> <font color="#ffffff">propagating towards the center of the Earth, this is our E field. We know that</font> <font color="#ffffff">the B field has to be at a right angle to the E field. Okay, so it can't be West</font> <font color="#ffffff">and it can't be East. We also know that it can't be up and it can't be down.</font> <font color="#ffffff">So the only option is into the screen or out of the screen.</font> <font color="#ffffff">It's either North or South, and if North is into the screen, let's see what we</font> <font color="#ffffff">would get, we would get E cross B, would get me a K that is pointing. Well let's</font> <font color="#ffffff">see, if we do this right. We've got -- we've got an E and then if B was coming in, it</font> <font color="#ffffff">would give me a K like that. So it looks like we do want a B field that is doing that.</font> <font color="#ffffff">Okay, we've taken this picture and we've rotated it to this, where the B is</font> <font color="#ffffff">going into and out of the board. So I would say, I would say that we need --</font> <font color="#ffffff">is that right? Hmm.</font> <font color="#ffffff">I think that's the wrong way. I think it's got to be this way</font> <font color="#ffffff">but you know what? Let's try it. So E going West means that the B field -- I'm gonna</font> <font color="#ffffff">say should be north. Let's just try it and see if we're right and if we're</font> <font color="#ffffff">wrong, it's probably the opposite which is south, and it says we are correct.</font> <font color="#ffffff">Okay, so B field is in fact in the north direction.</font> <font color="#ffffff">I might have tweaked this up a little bit but the important point is</font> <font color="#ffffff">we can eliminate west and east, up and down.</font>