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Physics32. Electromagnetic WavesEnergy Carried by Electromagnetic Waves

And let's ask the following question: what is the total -- what is the total power output of the sun? What is the total power output of the Sun? And let's say that we know a couple things. We're going to say that the intensity at the earth is equal to 1,390 watts per square meter, this is the intensity of the sunlight at the earth. All right, let's draw a picture of this thing. Here's our sun. Okay, it is spitting out electromagnetic waves in all directions. Some of those we collect right here on the earth. Okay, and we know that we are a distance, capital R, away from the sun. So if I want to think about how much power is emitted by the Sun in total, I have to worry about this sphere right here, of radius capital R. Okay, the total power emitted through that sphere is hopefully something we can calculate based on the intensity at the earth. All right, how do we do it? Well at the earth the intensity that we measure is just power over area and that is what we said was 1390 watts per square centimeter. But the total power coming out of the sun is going to be that intensity that we measure here, multiplied by the area of this giant sphere. Okay, we know S, what is the area of this giant dashed sphere? It is four PI capital R squared. Now take our little intensity and multiply it by the area of the sphere. And as you can imagine that's going to be a pretty big number so we have 1390 for S, we have a four, we have a pi, and now we need this number R, and this you can look up in your textbook -- how far is the Earth from the Sun? It is 1.5 times 10 to the 11 meters and so you're gonna square that. And somebody double-check my calculation, I ran this earlier but maybe you can double check, I get 3.93 times 10 to the 26 watts. Okay, 3.93 times ten to 26 watts for the total power coming out of the Sun, which is a pretty big number right? When we were talking about how much power your hairdryer uses, it was like one-and-a-half kilowatts, right? It was like 10 to the 3 watts and here's something that is 23 orders of magnitude bigger. It's not like you would expect -- it's lot of power coming out of the sun. Okay, but if that's the total power coming out of the Sun, let's ask a follow-up question. What is the intensity at the sun's surface? Okay, how do we do that? Well, we're going to need to know the radius of the Sun and if we do that, then we can calculate the intensity at the sun's surface, because it's just going to be that total power divided by the area of the Sun. And we know the total power, and the area of the Sun is four pi times the radius of the Sun squared. And so now again you can look up that number and let's punch it in right here. So P total we said was 3.93 times 10 to the 26 watts, we've got a 4 pi and then we have R squared, which if you look it up is 6.96 times 10 to the 8th meters. That's the radius of the Sun and if you put all this together you get 6.42 times 10 to the 7 watts per square meter. Okay, which is a big number, right? Think about a square meter, it's like that and it's going to have 64 million watts in that square meter, that is a lot of electromagnetic intensity.