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.