Intro to Electromagnetic (EM) Waves - Video Tutorials & Practice Problems

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Introduction to Electromagnetic (EM) Waves

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Hello, everyone. And welcome back in previous chapters, we learned a lot about mechanical waves. The classic idea we used over and over again was flicking a wave on a string up and down to create a disturbance. Now, we've also learned in recent chapters, a lot about electromagnetism. And in this video, I'm gonna put those ideas together to show you a new type of wave you'll need to know called an electromagnetic or sometimes called an em wave. For short, I'm gonna show you some key similarities and differences between these types of waves so that you can solve problems. All right. So let's jump right in. So remember that the whole idea behind a wave is that it is a traveling disturbance through space with our wave on a string, you flick it up and down and that creates an oscillation, that's a disturbance and it travels through space. So the big question here is, what exactly is the disturbance for this new electromagnetic wave? What's the thing that's sort of going up and down? Like the string was moving up and down? Well, as the name implies, the electro parts in electromagnetic means that it's an oscillating electric field. And likewise, the magnetic part of that word means there's also gonna be an oscillating magnetic field. All right. So that's the big idea. You have an oscillating electric and magnetic field. I'm gonna go ahead and show you what that looks like here with a mechanical wave. You just flick it up and down like this. What does it look like for an electromagnetic wave? Well, the first thing you'll notice is that you'll need a sort of 3D diagram to do this and I'll show you why in just a second. So basically, it actually looks very similar. It's gonna go up and down and up like this. So what's the thing that's moving up and down? Well, it's actually just the strength, the magnitude in the direction of the field itself. So basically what happens is that the fields oscillates by constantly changing magnitude and direction, what that means here is that on this wave, the electric field at this point points up and then it gets stronger over here, then it gets a little bit weaker and then eventually it actually just reverses and it points downwards and then the cycle repeats itself over and over again forever. So that's what's going on here. That's what's oscillating the strength and the direction of the field itself. Now, let's draw the magnetic field. All right. So that was e over here, let's draw with it field looks like. Now, the first thing you need to know is that these electric and magnetic fields are always going to be perpendicular. This actually comes from the right hand rule, remember, a changing electric field will produce a magnetic field. So basically what this looks like here is, it's gonna look like a perpendicular to up and down is gonna be back and forth. All right. So this is gonna sort of look like this. It's gonna look a little funny because of the perspective. It's not a diagonal wave, but instead going up and down, this wave is actually going forwards and backwards. All right. And I can show you that using these arrows to kind of make it a little bit more visually apparent that these things are actually going to be perpendicular. All right. So basically what this means here is that at any point, these arrows always have a right angle in between them, one's on the y axis and then one is on the Z axis moving back and forth. All right. So these fields are always perpendicular and that's basically what an electron magnetic wave looks like. You have an E field going up and down and a B field that's moving sort of forwards and backwards. All right. So the first thing we need to do is actually talk about the direction of these electromagnetic waves. So let's talk about the mechanical waves. Remember that mechanical waves, the direction was always perpendicular to the oscillation, the oscillation was up and down, that's where you flick the wave of the string up and down. But the direction was always sort of to the side like this. So that means that those were perpendicular. Well, for electromagnetic waves, it's very similar the electro uh for the direction it's gonna be perpendicular, but actually, it's gonna be perpendicular to both of the oscillations. What that means is that this wave here is gonna travel in a direction it's perpendicular to both the up and down oscillation of the electric field and also the forwards and backwards motion of the magnetic field. And the only two possible abilities or perpendicular to both of those things is either the wave is moving to the left or to the right. So which one is it, is it left or is it right? Well, like anything in electromagnetism to find a direction you have to use the right hand rule and it's no different here. We use the right hand rule over and over again. And there's one for figuring out the direction of electromagnetic waves. So to determine the wave direction, here's what you're always going to do. You're gonna take your fingers and remember it's always the best to do this yourself and you're gonna point them along the electric field. So for example, in this region over here, the electric field points up and then what you're gonna do is you're gonna curl your fingers towards the magnetic fields, you're gonna curl towards B and then your thumb should point in the direction of travel. All right. And if you do this, what happens is you gonna take your fingers curl, point them up, curl them towards you and your thumb should be pointing to the right. So what that means is that for this electromagnetic wave here, the wave is actually traveling to the right, this is the correct direction and it's not traveling to the left. All right, you can always use the right hand rule to figure out any two of these, sorry to figure out any one of these directions here. All right. That's basically the introduction to an electromagnetic wave. Let's go ahead and take a look at another example problem.

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Problem

Problem

You measure the electric field of an electromagnetic wave at a particular moment and find it points in the +z direction. The magnetic field points in the +y direction. In which direction is this wave traveling?

A

+x

B

+y

C

-x

D

-y

3

concept

Introduction to Electromagnetic (EM) Waves - Speed of Light

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6m

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Hello, everyone and welcome back. So in the last few videos, we saw how to find the direction of electromagnetic waves. But some problems like the one we're gonna work out down below will ask us for the direction and also ask us to relate the speed of the waves with the magnitudes of the fields that make it up. So what I wanna do in this video is I want to talk to you about the speed of electromagnetic waves and I'm gonna show you some very important equations you need to know to solve problems. Let's go ahead and take a look here. So remember that all waves travel at certain speeds and it really just depended on their type and also the environment that they travel through. For example, with mechanical waves, we had waves on strings, we also had ocean waves through water and we had sound waves through air and all of them had their different speeds. So actually what I first want to point out is the difference between mechanical and electromagnetic waves because mechanical waves did require a medium, they did require some type of material to travel through, right. So our waves on strings needed the string you have to have that the ocean waves require water to travel and sound waves require air to travel through without any air. There would be no sound and that's different from electromagnetic waves because electromagnetic waves do not require a medium. So for example, things like visible light from the sun or radio waves or even x rays don't require a material to travel through. So basically, it means is that these waves can freely travel through the vacuum of space. They don't need air or water or anything like that. All right. So let's move on here because for mechanical waves, the speed did depend on the properties of the medium itself. For example, with waves on strings, we saw this equation here not gonna write it out, right. Uh Which is the V string equation, which really just depended on the tension on the string divided by the mass and length of the string. So I'm just gonna make up some numbers here really quick here. If I was whipping the string up and down with a tension of 10 newtons, and let's say the speed of the wave was 5 m per second, then if I flicked it harder and basically flicked it with a tension of 40 newtons, let's say, then the wave speed would double, it would double to 10 m per second. All right. So that speed could change depending on the properties of the medium like tension or something like that. All right. Now, let's look at electromagnetic waves because electromagnetic waves, the speed also does depend on the medium. But there's a very important distinction here, which is that basically in your homeworks and your tests and things like that, the most of your problems are gonna involve electromagnetic waves that are traveling in a vacuum. So unless you are explicitly told otherwise, you can always assume that this is true, you can always assume that waves are traveling in a vacuum here. And that's really important because that means that the speed is going to be the same. In fact, we give this, this speed a letter, it's the letter C and it is always equal to 3.0 times 10 to the eighth. Uh oops that's 10 to the eighth meters per second. All right, this is a universal constant. Uh That is super important known as the speed of light in a vacuum. What it means is that all electromagnetic waves, whether it's visible light or X rays or radio waves or whatever, they will always travel at this speed here as long as they are in a vacuum. So what that means is that this electromagnet wave not only is traveling in this direction as we saw from the last video, but it's traveling with a speed equal to c which is just three times 10 of the 8 m per second. All right. So it's super important, you absolutely have to know that. Now, before we get to our example, I have one last thing to show you, which is that the speed here is also related to the magnitudes of the electric and magnetic fields that make it up. And the equation for that is that C is equal to E divided by B. So in other words, what happens here is that the ratio of the field of the magnitude of the electric field to the magnetic field at any point is always equal to C. All right. So this equation here is really important because basically what it means here is that if you have E divided by B, you should get 33 times 10 of the 8 m per second. What this equation allows you to do is if you're ever missing one of these variables, but you know the other one then you can always solve for whichever one you're missing, whether it's E or B. All right now, sorry. One last thing here is you may also see this expression written in your textbooks, this one over square of mu not or whatever. Uh This is something that you might just conceptually need to know. But basically these variables or these constants here are the permittivity and the perm permeability constants that we saw a lot in electromagnetism. All right. Now let's move on to our example here. So we have an electromagnetic wave that's traveling in the negative Z direction. So in other words, it's traveling sort of this way, it would actually sort of be into the page, um, sort of away from you. Right. So, at any particular, at a particular point in a particular instance, the electric field is along the x axis. So what I'm just gonna do here is I'm just gonna draw on the origin, I'm gonna draw that the electric field uh is gonna be along the positive axis and I'm not going to draw the wave itself. I'm just gonna sort of draw the strength of the field at this point. And this e here is equal to 500 volts per meter. Now, we want to do is we want to find the magnitude and direction of the magnetic field at this point. So in other words, we want to calculate what B is equal to. All right. So actually, we know how to solve for the direction of the magnetic field. That's what we saw in a previous video. We just use our right hand rule. All right. So let's actually solve for that first. So if we have the electric field and we know what the velocity here is, which is equal to, which is equal to C and we can figure out what the magnetic field is. Basically, if you want to point your thumb away from you and you want to point your fingers towards the electric field, then basically what that means is that the magnetic field should actually point like this. All right. So you should have this is your B field, it should point in the negative y axis like that, right? So if you point your fingers this way and curl towards this, your thumb should be pointing away from you. Again, the perspective is kind of where here? All right. So that means that the magnitude and so the direction is gonna be um direction will be negative Y axis. So what about the magnitude? Well, to do that, to find the magnitude, we're actually just going to use our new equation here, which is C equals E divided by B. All right. So if we have that C equals E divided by B and we can rearrange this equation and we can say that B is equal to E divided by C. So in other words, we have the uh we have 500 which is our electric field magnitude divided by the speed of light, which is three times 10 to the eighth. And what you should get here is you should get 1.67 times 10 to the minus six. And that's gonna be in tesla's. All right. So that's your final answer here. That's the strength of the magnetic fields. Um And it is pointing in the negative Y axis. All right folks. So that's it for this one. Let me know if you have any questions.

4

Problem

Problem

You measure the magnetic field strength of a traveling electromagnetic wave to be $8.0\times10^{-7}T$ , oriented along the +x direction. If this EM wave moves in the +y direction, what is the magnitude and direction of the wave's electric field at that same exact spot?

A

$240\frac{N}{C}$ in the -z direction

B

$2.4\times10^{-15}\frac{N}{C}$ in the -z direction

C

$240\frac{N}{C}$ in the +z direction

D

$2.4\times10^{-15}\frac{N}{C}$ in the +z direction

5

example

Example 1

Video duration:

2m

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All right, folks, welcome back. So let's check out this practice problem here. So we have a Martian rover that uses some radio pulses or signals which are electromagnetic waves to communicate with scientists. Back on earth, the pulses take about 12 minutes to arrive. So presumably once they hit the little button to transmit information, it takes 12 minutes to arrive. We want to calculate how far apart are Mars and Earth. So in this, the first thing you should realize is that they're not really asking you to compare the strengths of two fields together. We have no information about the electric or the magnetic field. So really this is sort of a different kind of problem in which it's really just testing you uh how you can use the information of the speed of light. So here's what's going on here. We know that the, the definition for velocity is that it's displacement over time, delta X over delta T. In this case though, we know that this is the V when we're dealing with electromagnetic waves is always going to be C which is the speed of light. So we can rearrange this equation and say that speed is equal to delta X over delta T. So we told basically how long it takes for the signals to get to earth that's delta T. And we know what the speed of light is, which is just a constant. So really what they're asking you to find is they're finding, you're finding delta X, how far apart are Mars and Earth? So I'm actually just gonna hide that light highlight that in yellow. So this is really just not really a new equation. It's just sort of like testing you on your knowledge of the speed of light. So let's just rearrange this equation here. Uh And so we're gonna have the delta X is equal to C times delta T. We studied motion in one D. This was usually a V velocity times time, but now we're just going to use C. That's all there is to it. All right. So first of all, uh before we actually start plugging anything in, we know what the speed of light is now, we just have to get the time because the time is actually not given to us in seconds, which is the si unit, the time is given to us in minutes, which is 12 minutes. So the first thing we have to do here is we just have to convert 12 minutes to seconds. And all you have to do is just multiply by 60 which is just seconds per minutes. You'll see the units cancel and you're gonna get that 720 seconds. So that's what you plug into this equation here. All right. So there's just one little extra step with some units here. Um And this is just gonna be three times 10 to the eighth and then you have to do 720 right? Because if you didn't multiply that, remember that the speed is given to us in meters per second. So you can't multiply meters per second times minutes. So you have to get it into seconds anyway, once you work this out here, what you're gonna get here is 2.16 times 10 to the 11th and that's in meters. This is perfectly sufficient to write down as an answer. Uh But this is also just if you convert it, this is also just equal to 216 million kilometers. All right, which is about reasonable for the distance between Earth and Mars. All right, folks, that's it for this one. Let's keep going.

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