Anderson Video - Intensity

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