Anderson Video - Electromagnetic Energy

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