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Physics32. Electromagnetic WavesEnergy Carried by Electromagnetic Waves

Electromagnetic energy. First off, let's ask you guys a question. Do electromagnetic waves carry energy? Sure. How do you know that? What happens when you go outside and sit in the sunshine, especially like today? What happens when you absorb a lot of sunshine? You get warm, right? You get hot. That's because those electromagnetic waves, which are coming from the Sun, Travel all the way across space, punch through our atmosphere, come down, hit you. You're absorbing it. You are absorbing that energy. You get warm. Okay, so electromagnetic waves clearly carry energy. And we talked about this a little bit before with the idea of water, right? Water is H2O. It looks like that but it also has a dipole moment to it. And so, if we flip this thing to the right, and then flip it to the left, and flip it to the right, and flip it to the left. We can do that. And you'll get a little seasick. But if you do that at a particular frequency. 2.4 gigahertz. This thing turning right and left. That is of course your microwave oven. Okay, there's an electric field that's gonna do that. And so, we can draw this electric field coming in to do that. Now if that electromagnetic field is carrying energy, which it is. It's transferring it to the water and that's heating up your food. So there is some electric energy density. Which we talked about before. And the electric energy density was the following. Remember energy density is just energy per volume. And we ended up with one-half epsilon naught E squared. In the last chapter, we talked about the magnetic energy density. How much energy is in a magnetic field? And that was 1 over 2 mu naught B squared. So the total energy density in a wave is just going to be the sum of those two. It's one-half epsilon naught E squared plus 1 over 2 mu naught B squared. But the two components have equal contribution to the overall energy density. So we have the caveat that the electric interview density is, in fact, equal to the magnetic energy density. And so, we can write the total energy in that wave. U is what we're calling the energy density. And we can write it in terms of E. And if the electric part is equal to the magnetic part, we can just write it as twice the magnetic part. Epsilon naught E squared. Or we can write it in terms of the magnetic part. 1 over mu naught B squared. Okay, and this is what we're calling U. The total energy density. Okay so we have equal parts E and B. But let's take a look at this last equation here and see if we can determine the relationship between E and B. So what we said was one-half epsilon naught E squared is the same as 1 over 2 mu naught B squared. Let's multiply by 2 on each side get rid of the half. And now let's divide by an epsilon naught. And now let's take a square root of both sides. Okay, but we know what these values are. We know what epsilon naught is and mu naught is. So this becomes the following. E is 1 over the square root of epsilon naught, which we said was 8.85 times 10 to the minus 12. Mu naught was 4 pi times 10 to the minus 7. Can somebody punched this stuff into your calculator and tell me what you get, and I will approximate it here. And hopefully you got that. Anybody get that number? When they did 1 over the square root of all this stuff right here? That's right? So this is kind of cool, right? c, the speed of light, came about from that. You take those electric experiments that you did. And you figured out what epsilon was. You did some magnetic experiments and you figured out what mu naught was. And suddenly, you put them together in this special way and you get the speed of light. You get how fast electromagnetic waves travel across the universe. And this is the beauty of Maxwell's equations and Maxwell's derivation of this problem. Before Maxwell, nobody really knew definitively that light was electromagnetic waves. And it was only after Maxwell that we knew that.