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Physics32. Electromagnetic WavesDisplacement Current and Maxwell's Equations

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