32. Electromagnetic Waves

Energy Carried by Electromagnetic Waves

Physics32. Electromagnetic WavesEnergy Carried by Electromagnetic Waves

Okay, let's think about intensity. So when we talk about electromagnetic waves and we talk about these things carrying energy, we need to talk about intensity of the electromagnetic wave. So you're familiar with this idea, right? When you go out and lay in the sunshine you get warm. Okay, but that sunshine that is hitting the ant on the ground warms up the ant. But if I take a big lens, all right, and I focus a whole bunch of sunlight onto that poor little ant, I can in fact burn up the ant. All right, you've probably done this experiment when you were kids. So what has changed? And what has changed is the intensity of the electromagnetic wave at that focal spot. So let's talk about intensity. Intensity, we actually are going to write with an S. Okay, and S is power divided by area. The reason that we use an S is this comes from something called the pointing vector and the pointing vector, traditionally they use an S. So power is P, area is A, but we know that power is energy per ton and we're going to divide that by area A. Okay, energy per time is the same as energy density times volume divided by time, times area A. Okay, and we know what some of these things are we. We know what energy density is. Energy density was our good old U. What about volume? Volume we're not really sure yet, so we'll leave it right there. Time is just T. So, what do we mean by volume? Well let's think about an electromagnetic wave propagating along. Okay, this electromagnetic wave propagating along is going to occupy a region of space that has a cross-sectional area A to it and it has a length here, L, which is equal to how fast it's moving for how long. It moves at C, it does that for a time T, that's the length of this box. So what's the volume of the box? Well it's just cross-sectional area A times the length L, so it is A c t. So what do we get here? We get U times the volume A C T and we're going to divide it by A T. The A's cancel out, the T's cancel out, and we just get U times C. Okay, so S is equal to U times C, but we know exactly what U is. U is one half epsilon naught E squared plus 1 over 2 mu naught B squared. But those are equal and so we can just double one of them, we can say S is equal to C epsilon naught E squared or S is equal to C over mu naught E squared. Those are equivalent statements. Okay, so with this information now let's see if we can understand something about our sun, how about something relevant to our particular situation on the earth, how about the Sun?