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Anderson Video - Electromagnetic Wave Example

Professor Anderson
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<font color="#ffffff">In an electromagnetic wave traveling west,</font> <font color="#ffffff">The B field oscillates up and down vertically and has a frequency of 93 kilohertz</font> <font color="#ffffff">and an rms strength of 7.15 times 10 to the minus 19 teslas.</font> <font color="#ffffff">Assume that the wave travels in free space.</font> <font color="#ffffff">Okay, and part A says, "What is the frequency of the electric field?"</font> <font color="#ffffff">Okay so let's start with Part A.</font> <font color="#ffffff">Okay, we have an electromagnetic wave and it says that we're gonna describe the B field.</font> <font color="#ffffff">And the B field that we drew before was going in and out of the board so let's draw the whole thing again.</font> <font color="#ffffff">Here was our E field going up, going down, going up and down.</font> <font color="#ffffff">And the B field was coming in and out of the board.</font> <font color="#ffffff">Okay, E going up.</font> <font color="#ffffff">B, like that.</font> <font color="#ffffff">So the first thing they tell us is the B field oscillates with a frequency of 93 kilohertz.</font> <font color="#ffffff">So if the B field is oscillating at 93 kilohertz, what do you think the frequency of the electric field is?</font> <font color="#ffffff">What do you think?</font> <font color="#ffffff">>> (student speaking) 93.</font> <font color="#ffffff">>> Got to be the same, right?</font> <font color="#ffffff">I mean look at the picture.</font> <font color="#ffffff">E is going up and down at exactly the same rate as the B is going.</font> <font color="#ffffff">So this has to be 93 kilohertz as well.</font> <font color="#ffffff">All right, let's try it.</font> <font color="#ffffff">93.</font> <font color="#ffffff">Let's see if it'll take a kHz for our kilohertz.</font> <font color="#ffffff">And in fact it does.</font> <font color="#ffffff">And it says we are correct.</font> <font color="#ffffff">All right, Part B says, "What is the rms strength of the electric field?"</font> <font color="#ffffff">And what they gave us was the strength of the B field rms.</font> <font color="#ffffff">And they told us it was 7.15 times 10 to the minus 9 tesla.</font> <font color="#ffffff">And so now we're looking for E rms.</font> <font color="#ffffff">Hmm.</font> <font color="#ffffff">Well we're not really sure how E relates to B yet. But if we push forward a little bit</font> <font color="#ffffff">in the discussion, there is a very nice and simple relationship between E and B.</font> <font color="#ffffff">And let me pull it up here.</font> <font color="#ffffff">And this is going to be a little bit ahead of ourselves but we'll get back to it in a second.</font> <font color="#ffffff">What we can say is the following.</font> <font color="#ffffff">The energy in the E field is in fact equal to the energy in the B field.</font> <font color="#ffffff">And those things relate to each other by the speed of light.</font> <font color="#ffffff">So what is the electric field?</font> <font color="#ffffff">It's equal to c, the speed of light, times the B field.</font> <font color="#ffffff">Okay?</font> <font color="#ffffff">So, E rms is just equal to C times B rms. So if I take this value of B </font> <font color="#ffffff">and I multiply it by C, 3 times 10 to the 8 meters per second, we're gonna get the right answer.</font> <font color="#ffffff">Okay, and if somebody wants to try that in your calculator.</font> <font color="#ffffff">Tell me what you get.</font> <font color="#ffffff">Should be about, what's that?</font> <font color="#ffffff">3 times 7 is 21. And then we've got </font> <font color="#ffffff">3 of those 15s, which is the 0.45, and then we've got a 10 to the minus 1.</font> <font color="#ffffff">So I'm gonna say this thing is 2.145.</font> <font color="#ffffff">And it's the value of electric field which is, of course, volts per meter.</font>