Intro to Electromagnetic (EM) Waves - Online Tutor, Practice Problems & Exam Prep

Introduction to Electromagnetic (EM) Waves

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 going to 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 going to show you some key similarities and differences between these types of waves so that you can solve problems. Alright. 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 part in electromagnetic means that it's an oscillating electric field. And likewise, the magnetic part of that word means there's also going to be an oscillating magnetic field. Alright? So that's the big idea. You have an oscillating electric and magnetic field. I'm going to 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 going to 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, and the direction of the field itself. So basically, what happens is that the fields oscillate 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. Alright. So that was E over here. Let's draw what the B 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 going to look like perpendicular to up and down is going to be back and forth. Alright? So this is going to sort of look like this. It's going to look a little funny because of the perspective. It's not a diagonal wave, but instead of going up and down, this wave is actually going forwards and backwards. Alright? 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. Alright? 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. Alright? So these fields are always perpendicular, and that's basically what an electromagnetic wave looks like. You have an E field going up and down and a B field that's moving sort of forwards and backwards. Alright?

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, 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, for the direction, it's going to be perpendicular, but actually, it's going to be perpendicular to both of the oscillations. What that means is that this wave here is going to travel in a direction that's perpendicular to both the up and down oscillation of the electric field, and also the forwards and backward motion of the magnetic field. And the only two possibilities for 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 going to take your fingers, and remember, it's always best to do this yourself, and you're going to point them along the electric field. So for example, in this region over here, the electric field points up. And then what you're going to do is you're going to curl your fingers towards the magnetic field, so you're going to curl towards B, and then your thumb should point in the direction of travel. Alright? And if you do this, what happens is, you're going to take your fingers, 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. Alright? You can always use the right-hand rule to figure out any one of these directions here. Alright? That's basically the introduction to an electromagnetic wave. Let's go ahead and take a look at another example problem.

Intro to EM waves Example 1

So let's try this next example problem here. We're told that the electromagnetic wave travels in the plus z direction. Remember, these things are always kind of tricky because we're looking at a three-dimensional coordinate system on a two-dimensional page. Basically, what this means here is the z direction sort of points out at you from the page. We're told that the electric field oscillates along the plus x-axis.

So, in other words, right here, it oscillates left to right, so in this horizontal axis over here. And we're going to draw the magnetic field. How does the magnetic field look like? And it would just have to be a sketch. It doesn't have to be perfect.

Okay? Remember that the relationship between magnetic fields, electric fields, and the wave direction, the wave that it travels in, is all really related by the right-hand rule. And it's always best to do it yourself. Don't just look at me. Okay?

So your thumb is going to be pointing out towards you. And so we want to figure out where your fingers are and where you're going to have to curl towards to find the magnetic field. Alright? So I want you to take your right hand. To me, it looks like my left, but this is actually my right.

And I'm going to point at me so that my thumb points at myself. Alright? You always want to do this. And now what I'm trying to do is I'm going to try to align my fingers so that it points off to my right because that's where you want your fingers to point along the x-axis. So this way is where your fingers are going to point.

Again, it's always better to do this yourself rather than look at me. So to you, what happens is when I do this, it looks like my fingers are pointing off to the left, but to me, they're actually pointing off to my right. So then what direction would I have to curl? What direction are my fingers going to curl in so that my thumb is actually pointing at me? They're basically going to curve upwards.

So, basically, what happens here is I'm going to have to curl towards this axis, the y-axis over here. And so my magnetic field is going to look something like this. Alright? So remember, it's kind of going really up and down. That's kind of the direction that this thing is oscillating in.

And I'm going to draw these arrows up here like this. Alright. So it's going to be up over here, and then it's going to be down over here. It kind of looks a little wonky because of the perspective, but, really, this wave is oscillating up and down, whereas the electric field is oscillating to the left and to the right. Okay?

So in other words, this is the direction over here of the magnetic field. This is the direction where your fingers are going to curl in. Okay. So this is really the answer. This is the direction of the magnetic field over here.

Let me know if you have any questions, and let's keep going.

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

Introduction to Electromagnetic (EM) Waves - Speed of Light

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 going to 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 want to do in this video is I want to talk to you about the speed of electromagnetic waves, and I'm going to show you some very important equations you need to know to solve problems. Let's go ahead and take a look here.

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 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. Now, 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. 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 that these waves can freely travel through the vacuum of space. They don't need air or water or anything like that.

Now, 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. I'm not going to write it outright, 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 going to make up some numbers here really quick here. If I was ripping the string up and down with a tension of 10 Newtons, and let's say the speed of the wave was 5 meters 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 meters per second.

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, most of your problems are going to 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 speed a letter, it's the letter c, and it is always equal to 3.0×108m/s. This is a universal constant, 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 electromagnetic 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 3×108m/s.

Now, before we get into our example, I have one last thing to show you, which is that this 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'. This equation here is really important because basically what it means here is that if you have e divided by b, you should get 3×108m/s

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

Example 1

Welcome back. Let's check out this practice problem. So, we have a Martian rover that uses radio pulses or signals, which are electromagnetic waves, to communicate with scientists back on Earth. The pulses take about 12 minutes to arrive; presumably, once they hit the little button to transmit information, it takes 12 minutes to arrive. We want to calculate how far apart Mars and Earth are. In this problem, 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 just testing how you can use the information of the speed of light. So here's what's going on here. We know that the definition for velocity is that it's displacement over time, delta \(x\) over delta \(t\). Although, in this case, we know that this \(v\), 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 \(t\). Basically, we’re told 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, what they’re asking you to find is delta \(x\), how far apart Mars and Earth are. So let's rearrange this equation here, and so we're going to have delta \(x\) equal to \(c\) times delta \(t\). In our typical studies of motion in one dimension, this was usually a \(v\), velocity times time, but now we're just going to use \(c\). That's all there is to it.

First of all, before we start plugging anything in, we know what the speed of light is. Now we just have to get the time because the time is given to us in minutes, which is 12 minutes. The first thing we have to do here is convert 12 minutes to seconds. All you have to do is multiply by 60, which is seconds per minute. You'll see the units cancel, and you're going to get 720 seconds. That’s what you plug into this equation here. There’s just one little extra step with some units here, and this is just going to be \(3 \times 10^8\) and then you have to do 720. Right? 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 going to get here is \(2.16 \times 10^{11}\), and that's in meters. This is perfectly sufficient to write down as an answer, but this is also, if converted, just equal to 216,000,000 kilometers, which is about reasonable for the distance between Earth and Mars.

That's it for this one. Let's keep going.