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A sinusoidally varying ectromagnetic field propagates through a window of area 0.40 m?. Ifthe amplitude of the electric field is 0.50 Vlm; what is the average energ...

Question

A sinusoidally varying ectromagnetic field propagates through a window of area 0.40 m?. Ifthe amplitude of the electric field is 0.50 Vlm; what is the average energy per unit time (power) that is being transmitted through the window; in W?1.3X 10-41.8 X 10-4 2.4 X 10- 4 9.1 X 10-56.4 X 10-5

A sinusoidally varying ectromagnetic field propagates through a window of area 0.40 m?. Ifthe amplitude of the electric field is 0.50 Vlm; what is the average energy per unit time (power) that is being transmitted through the window; in W? 1.3X 10-4 1.8 X 10-4 2.4 X 10- 4 9.1 X 10-5 6.4 X 10-5



Answers

A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area $0.500 \mathrm{~m}^{2}$. At the window, the electric field of the wave has rms value $0.0200 \mathrm{~V} / \mathrm{m} .$ How much energy does this wave carry through the window during a 30.0 s commercial?

In this problem will be taking a look at energy transfer through electromagnetic waves. So in this scenario, we have a window with a cross sectional area of five square meters, and we have a sustained source of light coming through this window. And we've measured the electric field, Um, on average, Meaning root, mean square, um, to be of value, which is 0.2 full meters and the way to go from root mean square to, um, the max energy that is in the equation that you might be familiar with, which, all right down here, um, which is that I equals one half, um, Epsilon, Not permissive ity times the speed of light times E max. Which is kind of what we're interested in that year. The way to go from our MST max is to take RMS. So let's say E r mess is equal to e max divided by the square root of two. Because this is a average value that is convenient for everyday measurements. So we have this information here, so let's use that, um, to find out the total energy transfer and what I mean by energy transfer is work. So work is power over time. This year is essentially power per area. So what we want is this power. So we need to multiply this intensity by area to get power, and then we have to multiply power by time to get work. So let's let's do that so we can plug in, Um, for i t to use this given value. Varmus. So we're gonna have, um, essentially route two squared, which is to So it's gonna be to over to times e not time. See, kinds e are a mess, which you, I'm sure will notice, Is simply, um do you not see times e r mess? So that's our, um, intensity. So if we want to straight away get our power from this, we can just multiply by a which we were given up here. So then, in order to get work, we just need to multiply this p by time. So it's gonna be e not time, See times e r. Miss squared. I had to put that squared in there from right here. Um, times a times time. So let's write this whole thing out with the numbers plugged in. So it's gonna be 8.85 times e to the negative 12 for permissive ity of free space times three point or three times 10 to the eighth meters per second times this armistice value your 0.2 square times 0.5 m squared times 30 seconds because that's the duration of the time that this light is coming through the window. So in total, for a result, the value that you're gonna get is going to be 15.9 micro jewels, not that much energy.

Hello everyone, This problem whereas to find the energy delivered by a radio station through broadcasting its signal through a window of a given size or given surface area. So some basic information for the problem that we're gonna need are the speed of light which is 3.0 times that 3 m per second. The area of the window, which is given to be 0.500 m, squared the R M s um, after that a field amplitude which is given to be 0.200 wall square meters, the time of the commercial 30 seconds, and the primitive ity off vacuum which is 8.85 times centered in minus 12 for aspirin meters. Okay, so our objective is defined what Delta he is. And in order to answer this question, we need to know what the intensity is because we know that the intensity is the change or the the energy delivered per area per unit time. And so, if we are given an area and were given a time, we can find out through the intensity how much energy debate delivers. Okay, so first we need to figure out what the, um intensity is. And so the intensity in terms off the maximum electric field amplitude is given as a half time. See, time's absolute zero times e m x squared. But then how do we find MX? So the RMS Field amplitude is just 1/2 times the maximum field amplitude. So then putting this RMS or uh putting, uh, putting the are using this formula, we can write the intensity in terms of R. M s squared instead of m x squared as this sport over here. So the intensity in terms of the RMS field value is see, time's absolute zero times e or M s squared. Okay, so now that we found I, we can find that the delivered energy that e is equal to a that are a window times Delta t types of are in the time of the commercial times the intensity and then putting in the values off E. R. M s and excellent zero and see and all the t n A. We find that the energy delivered is 15.9 times center, minus six jewels

Hi there. So for this problem we need to calculate the energy of the wave that carry through the window and during a time of 30 seconds self We are also given the area of the window which is 0.5 m square. And we all also give and the electric field of the wave. Um the Earth M. A. S. Value which is er M. S. Volume. It is 0.04 hold his per meter. So to solve this problem is very straight forward. We just need to use one formula. And the first thing that we need to assume is that the area is normal to the direction of the wave so that the energy transported if the area times the magnitude of the point in bed wars times the time. So the pointing back to or in this case the magnitude of the point in Bhaktapur is given by the credit of the permeability of the vacuum, permissive. Itty um times the speed of light times the value of them electric field that in this case is the Earth M. S. Volume. So as I said, the energy in of this, it's just given by the area behind the magnitude of the pointing back towards times the times t. So we're gonna just put all of these values in here. Yeah, it is a .85 times 10 To the -12. Paradise eight Per meter. We also have d um a speed of line put in here which is three times sent to the aid meters per second and the value of the Electric fuel which is 0.0 four Bolt, is a meter, and finally the time, which in this case is 30 seconds. So from here we obtain a value of The result is one point find, 93 Times 10 to the -3 jewels. Or we can write it also at one point fine 83 milli tools. So this is the energy passing through the window. Yeah.

The formula we're going to solve this problem is that the total internee is equal to the intensity times, the area times the time. And so let's use the information. They give us the maximum electric field to figure out the intensity. We know that the two are related with this formula. Here, the intensity is 1/2 times the electric, constant time, speed of light times, the maximum electric field. But in this problem, we're actually giving the ROMs electric field, not the Maxwell, not your field. So we need to use the relation that they are. Mass electric field is equal to the max over the square two. Since you're a mess is smaller than E. Max. We're dividing by number greater than one. And so bringing this over here, we can plug in What the max is here, What we do that we get that the intensity is eagle to absolutely not times speed of light times. They are miss Electric field squared and so were given enormous. And so we consult for the intensity. And so the energy, the total energy here is equal to just going to take this guy here, and somebody in there and so you will not see e Armas squared Time's area times time. Now give us the area the window and give us that the times 30 seconds since it's a 32nd commercial, and so we can just plug in everything we know at this point. When we do that, we get that the total energy is 15 0.9 my her jewels, and so it's quite small, and that's final answer.


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