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Cc2-94/ Suppose the electric field of an plane E.M. wave has amplitude a. Determine the amplitude of the magnetic field. (a) Determine the time-averaged energy den...

Question

Cc2-94/ Suppose the electric field of an plane E.M. wave has amplitude a. Determine the amplitude of the magnetic field. (a) Determine the time-averaged energy density. (b) Determine the time-averaged energy flux:

cc2-94/ Suppose the electric field of an plane E.M. wave has amplitude a. Determine the amplitude of the magnetic field. (a) Determine the time-averaged energy density. (b) Determine the time-averaged energy flux:



Answers

The amplitude of an electromagnetic wave's electric field is $200 \mathrm{~V} / \mathrm{m}$. Calculate (a) the amplitude of the wave's magnetic field and (b) the intensity of the wave. Example $22-4$

Question belongs to the electromagnetic wave in which we have frequency F equals to 2.0 repair bait and to the power 10 herds and amplitude of the electric field in auditing equals to 48 volt meter. Universe. Okay, so for the part we have to determine the wavelength of the wave that is lambda. So we can say that the wavelength of the wave linda it is equals to see by frequency. So C. Is the speed of light. So 3 to 10 to the power eight m per second. They were a frequency which is 2.0 replied 10 to the power 10 words. So from here after solving we get prevalence λ,, it is equals two 0.015 m. So this become the answer for the part of the problem. Okay now for the part B we have to determine the amplitude of facilitating magnetic field that is being not. So we can write that. He not. It is he's not a verb. I see. It is equal to be not so from here after substituting values so be not. It is equal to the not with just 48 divided by C. Which is the speed of light. So three and 2 10 to the power eight m per second. So from here we get the not it is equal to 1.6 to 10 to the power minus seven Tesla. So this becomes the answer for the part B of the problem. Okay now moving to the part C. In which we have to show that the average energy density of the electric field that is you E. This is equal to Aboriginals intensity for the magnetic field. That is you be. So we know that you e. It is equal to one by two, absolute not manipulated by the knot. Is clear. And you be it is equal to one by two ab salad. One by two. Be not square divided by mu. Not Okay. And the speed of light. See it is equal to one by it is equal to one by one. The root of mu not replaced by C. Note. And also we have this relation. Okay so from here we can write that note. It is equal to be not manipulated by sea. So now substituting values so we will move from here. So after substituting the values so we will get that in this value. So he not it is equal to be not manipulated by sea which is this value. So one by you not manipulated by someone. Not in this under oath. So squaring on both sides. So we get the not square. This is equal to be not square divided by mu. Not manipulated by someone not so rearranging the situation so we get excellent note replaced by not square. This is equal to be not square develop new. Not now. But applying both situations. Both sales by one by two, so one by two and this one by two. So this term it is equal to U. E. So we can write it as U. E. And this is a term which is equal to you be. So this is the proof that both energy densities are equal. Okay.

In this question, we have an electromagnetic wave, Mhm. Drama. Uh huh. Um MPT after electric few. Uh Mx is sharing 30 watts per meter. So we want to find out Mp two of the corresponding magnetic field. So to do this question, we'll be using um E makes because to see B max. So BMX, which is the Mp two of the men and the magnetic field is Imex over. See Which is 330, divide by three times 10 to the Power eight. So we have 1.1 times 10 to the power of -6 Tesla. So this is the answer for this question. And that's all. Mhm.

Hi in this given problem here expression for the magnetic field oscillation in the electro magnetic way that is given as it is given as a function of the position and the time. So this is B. X. D. Is equal to 0.7 Micro Tesla sign eight by Into 10. If the power six per meter In two x minus 2.40 Bye Into 10 days. The power 15 per second. T. Now comparing it with the standard equation B X. D. Is equal to be not completed of the magnetic field means the maximum possible value into sign of K. X minus omega T. Where K. Is the wave number omega vista angular frequency. So comparing these two equations in the first part of the problem, complete your of magnetic field here Will come out to be be not a sequel to 0.7 micro Tesla which becomes the answer for the first part of this problem. Then in the second part of the problem we have to find the speed of this magnetic field. You're using K is equal to eat. Bye into 10 parts six parameter and oh Mika is equal to 2.40 pi Into 10 part 15 per second. Using these two values C means the speed of this. Andy will be given by the ratio of omega with the K. And here it is 2.40 by Into 10 days. Part 15 for a second Divided by gay which is 85 Into 10 days per six were meter. So finally here it will come out to be three into 10 days for eight meter per second, which is the answer for that second part of this problem. Now, in the third part of the problem here, we have to find frequency of this magnetic here, for which we will use a relation between angular frequency and frequency omega is going to be F. So using that we get an expression for the frequency f equals to omega by two pi. Now the value of Omega, this is 2.40. Why? in 2 10 days about 15 for a second divided by two pi. So here this frequency comes out to be 1.20 Into 10 days. Part 15 carbs Answy for the 3rd part of this problem. Then in the fourth part of the problem, we have to find period of the way yet. This period means time period which is given as the reciprocal of frequency inverse of frequency means this is one by 1.20 into 10 days. The power 15 second. So it will be calculated to be equal to 8.3 Into tended bar -16 second. Answy for the 4th part of this problem. And in the end, In the 5th part of the problem we have to find wavelength of this magnetic grip for which we will use an expression for the wave number which is given as capable to buy by lambda. So lambda will be two pi by K. It is too bye bye. Forget this is it. Why? In 2 10.6 four metre, so very violent here will come out to be 2.5 into standish for -7 m, which becomes the answer for the 5th and the last part of the problem. Thank you.

Energy and streets card too, Have absolutely not. He spent. So when are you? Density is given one dual per meter cubed. Absolutely not. 8.85 10 to the par minus spirit. And it is square electric. Create Bellamy 147 10 to the power six Bold perimeter and magarri feet. You can find E upon C 547 10 to the power six upon three into 10 to the power age. So it is to be 1.57 10 to the power minus three. Tesla. That's thanks for watching it.


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