5

Isotropic electromagnetic waves expand uniformly outward in all directions in three dimensions. Electromagnetic waves from a small, isotropic source are not plane w...

Question

Isotropic electromagnetic waves expand uniformly outward in all directions in three dimensions. Electromagnetic waves from a small, isotropic source are not plane waves, which have constant maximum amplitudes.a) How does the maximum amplitude of the electric field of radiation from a small, isotropic source vary with distance from the source?b) Compare this with the electrostatic field of a point charge.

Isotropic electromagnetic waves expand uniformly outward in all directions in three dimensions. Electromagnetic waves from a small, isotropic source are not plane waves, which have constant maximum amplitudes. a) How does the maximum amplitude of the electric field of radiation from a small, isotropic source vary with distance from the source? b) Compare this with the electrostatic field of a point charge.



Answers

Isotropic electromagnetic waves expand uniformly outward in all directions in three dimensions. Electromagnetic waves from a small, isotropic source are not plane waves, which have constant maximum amplitudes. a) How does the maximum amplitude of the electric field of radiation from a small, isotropic source vary with distance from the source? b) Compare this with the electrostatic field of a point charge.

In part a of this problem. We have to calculate the African sea off the bed. So we need to find yourself. And this is going by F vehicles to city wanted by Lambda. When he sees the screen off light in vacuum and one dies, It's well planned by sitting you Alice into the square weaken. Right It is 3.0 multiply laboratories parted meter per second. You wanted by We have the Waveland has three point boy for digital multiplied by terrorists bar minus two. So this would you of the value for F F F vehicles to seven point it one multiplied by terrorists. Mineards What? In part B of this problem, we have to kill Claire after July magnetic field. But is what we call be. Not so we can white. It is a B not equals two. This is the maximum temperature off this Byfield. So this is equals toe. You know he wanted by sea where they seized us. We don't like and you notice that maximum amplitude off. Like to feed my way. Inserting values into the square. Reagan White It is one point 35 hold perimeter you wanted by 3.0 multiplied with generous par eight meter particle. So this will give us the weather for the notice being articles too. 4.50 Multiply by to his bottle minus nine. Tesla What? Knowing Parsi, we have to kill Played the intensity over you Slide beam So we're ideas equals to whatever too. And then it's no, not Stevie, you know, square when this absolute not is the permitted off respects. Now, in setting the waters into the square, we can write It is I equals two whatever too, and then be of value for its no notice. Add pointed five multiple opportunities far minus 12. Well, im squared for new 10 meters square, we have the value for C as a 3.0 multiplied returns part. It may depart second and you know it is one point 35 per meter. This is square. So this would you want value for eyes cycles too. 2.42 Multiply bitterness par minus tree water per meter square. In party of this problem, we have to calculate that every forcing it exerts. So in d V have to calculate this effort bridge. So this forces given by Brexit multiply way area but disputes depression and a the all Kontic a surface area. So what, it's gonna be region as a I see the wanted by idea wanted by sea find it area because this pressure is equals to I do want it by sea But this eyes they against you off is light When setting Williams into the square Reagan white, fl radicals to we have the value for I as we have concluded in the previous section 2.42 multiply with Tunis Bar minus three. What put me to square. And, uh, today's zero point 240 meter square and we know that speed off light is there. 3.0 Montclair returns. Bar it, Mr Barsky. So this review on the radio for forces affect radicals to no one point 94 Much flour Tunis far minus 12. New dead. Thank you

For Barack scattering. We have the Maxima occurring in two D o. A scientist. Ada is equal to L'm Landa, and so they must satisfy this relationship. In part A. We have Emma's eagle one since we're told us the first maximum. So the order must be won. And we want to sell for the spacing between the planes, which is D and so solving for Deion. This equation gives l'm Lambda over to sign data. Liking him is a little one just removes them so we'd get slammed over to something. And then now we can plug in what lambda and they are so 0.173 times 10 to minus nine meters over sign of 22 0.4 degrees. This gives a de value of 0.227 meters, which completes hard, eh? Come on in Part B, we want to figure out what the angle is for. M is equal to two. So if the order raises up to two, what is the new maid? Well, to this we're just going to use this and we're gonna sell for Cynthia. So signed Ada is equal to own land over to D. We figured out. What do you owe us here? We know what Lambda is and now were going to plug into for him. And so when we do that, we get that data is equal to 49 0.6 degrees. And so that's why the thing is, when there was he going to Now can we have it so that it was equal to three. We'll be plugging in three for a film. You get a number here greater than one, and the sign of an angle could never be greater than one. So it was equal to three for all the numbers higher than to yield no solution. So we only see peaks at thes two locations at this data and at 22 point for those were the only two that work. And so that's the end of the problem.

Hi. In a given problem, the frequency off standing electromagnetic waves he's given us F is equal to 750 megahertz. We know in stationary waves or in standing graves. The points at the notes always remains addressed. They do not vibrate. So actually, in the given problem, we have to find the position off note because the charge kept at the position off north will remain addressed. It will not vibrate, so to find it. First of all, we should find the wavelength off this electromagnetic standing way, using the expression using the relation between the wave velocity and frequency and wavelength. It says C is equal toe if lambda So they've lamp comes out Toby. See by F where C is the speed off electromagnetic waves which is always equal to the speed off light in three into tended bar eight divided by frequency, which is 7 50 megahertz or 7 15 to 10 days apart. Six hers and that waas meter per second. So finally this reverent comes out Toby three. Bye. 7.5 neater. Or we can say this is 0.4 meter or 40 centimeter. No, as these are the conducting planes at a gap off 80 centimeter. The wavelength of the wave. The standing rape is 40 centimeter means a complete wave comes here exactly at the midpoint between these 80 centimeter having a wavelength off 40 centimeter. And this is another way. And as this is our standing with it can be represented like this. So all the charged particles situated at the points off notes will remain addressed. So as a total gap is 80 centimeter. So the land off one loop or we can say the distance between nearest nodes is equal toe half off. Violent means 40 by two means this is 20 centimeter. So the first charge, the position of first charge which is addressed, will be at a distance off 20 centimeter from the first conducting plane. And this is the answer for the given problem. The position off the point where the charge kept will remain addressed. Thank you.

This problem was what? Standing waves. Specifically, we're talking about electromagnetic waves which accomplish a standing state. Um, and the way that happens is you have incident waves coming in. They hit some conductor, which is able to reflect the radiation back out. And then the reflected waves interact with the incident. Incoming waves to form a standing state superposition of the incident and the outgoing that is stable. And that's what we call a standing electromagnetic wave. And so what? The question nous here is were given a frequency for this incoming wave, Um, were given that it's 75 75 megahertz, 75 megahertz. So that's the frequency of this radiation coming in. And the question is, how far apart are the nodal planes of these? Um, of the e component and the magnetic field component. And what they mean by nodal plane is what are the places that this component hit zero in the X domain. So I've drawn it out for you here. You can see that every time e that sign of K X equals zero, which corresponds to like, for example, if you have sign of one pie sign of two pi and so on, um that those are gonna be zeros. And so those air what you would consider to be nodal planes, it really doesn't want me to erase that. I guess I'll just do it the old fashioned way. So those are the nodal planes. And so one way you can figure out the distance between these nodal planes is to look at the frequency and say, Well, I mean, I know the frequency. I know that si is equal to f times lambda. So from F, I can get that lambda is equal to 4 m. Okay, so that means that every time ah, one every half wavelength Ah, we get one of these noted planes. So that means that the distance for E between these Notre planes is land over to or if you were to calculate that number, it's gonna be 2 m. Um, Similarly, for this scenario, every time co sign of K X is equal to zero, you'll get a zero down here and that's a no till plane for B. Um and there's also a distance of 2 m or half a wavelength between these Notre planes. And but now the question is what is the distance between a nodal plane, the closest distance between the nodal plane for eat and for be well, the distance between here and here's to the distance between are here and here is to so you can see pretty clearly that the distance between nodal plains of E and B is one 1 m. Because you have one right here and you have one right here. These air to part these air two parts of this is right in the middle, a distance of 1 m.


Similar Solved Questions

5 answers
Delermine tne product(s) formed in each reaction.NeS
Delermine tne product(s) formed in each reaction. NeS...
2 answers
0 f $ Z00 nue sted C +o4c | Iodica 1ao I6 S: i^ +w0 ntcrc $ + annucl4 Cx) eared 5 / b anl( acCont One 61 annvaliy Cy) earaed AC ( Ovnt the o+hcr from bc th Ind.c^ earacc To +4 | amount The LJ ^ $ 177 Q € € 0n+ 0f+cr OAc yeac cn $ Shols how~ which Se+ 0 f ecuch O eech a €Cc-nt mcch L Crc Pc+AX+ Y = 300 5x +6y = 17 12 X+ Y =300 0, 05 K + 0.o6 Y 317 C' K+Y - 17 5/ + 6Y- 300 p: X + Y = 17 0,05X + 0.0 6Y 30 0
0 f $ Z00 nue sted C +o4c | Iodica 1ao I6 S: i^ +w0 ntcrc $ + annucl4 Cx) eared 5 / b anl( acCont One 61 annvaliy Cy) earaed AC ( Ovnt the o+hcr from bc th Ind.c^ earacc To +4 | amount The LJ ^ $ 177 Q € € 0n+ 0f+cr OAc yeac cn $ Shols how~ which Se+ 0 f ecuch O eech a €Cc-nt mcch ...
5 answers
ImntIe rvzlue of the key polnts below, which are on the graph of the logarithmnic functionlog! ()Provde your answer below:Rey Pointe) uu (|
ImntIe rvzlue of the key polnts below, which are on the graph of the logarithmnic function log! () Provde your answer below: Rey Pointe ) uu (|...
5 answers
If the rate law of a reaction $mathrm{nA} longrightarrow mathrm{B}$ is expressed as Rate $=-frac{1}{n} frac{d[A]}{d t}=+frac{d[B]}{d t}=k[A]^{x}$The unit of the rate constant will be(a) $mathrm{mol}^{mathrm{x}} / mathrm{L}^{mathrm{x}} / mathrm{s}$(b) $mathrm{L}^{mathrm{x}} / mathrm{mol}^{mathrm{x}} mathrm{s}$(c) $operatorname{mol}^{(1-x)} / L^{(x-1)} cdot S^{-1}$(d) $m o l^{(x-1)} / L^{(1-x)} cdot S^{-1}$
If the rate law of a reaction $mathrm{nA} longrightarrow mathrm{B}$ is expressed as Rate $=-frac{1}{n} frac{d[A]}{d t}=+frac{d[B]}{d t}=k[A]^{x}$ The unit of the rate constant will be (a) $mathrm{mol}^{mathrm{x}} / mathrm{L}^{mathrm{x}} / mathrm{s}$ (b) $mathrm{L}^{mathrm{x}} / mathrm{mol}^{mathrm{x...
5 answers
0t The /ta.& 0ass"5 thvev0 5 Fma Th< eqvat'- 474 prv Prndvevlaz t0 the kch -< The 06h + (2,9,') X= J+) Y= 2-t 2 = 3 + 4f 74,'6" Fina eqstven cf T4€ fls*€ .
0t The /ta.& 0ass"5 thvev0 5 Fma Th< eqvat'- 474 prv Prndvevlaz t0 the kch -< The 06h + (2,9,') X= J+) Y= 2-t 2 = 3 + 4f 74,'6" Fina eqstven cf T4€ fls*€ ....
5 answers
10. Using Laplace transforms, find the solution of the initial value problemdv dt22v = 2us(), 4(() =0 v(0) =%
10. Using Laplace transforms, find the solution of the initial value problem dv dt2 2v = 2us(), 4(() =0 v(0) =%...
5 answers
40 Pb 3 Skow Fh ak 2 24 x | x -0~E e Je
40 Pb 3 Skow Fh ak 2 24 x | x -0 ~E e Je...
5 answers
Classly Uie TOlOWIg amio acias On the Dasics 0f thenr side group-Polar; nonpolar; positively or negatively charged:Thls PhotoUnknown Author Isoh C, Ch;HoHiN _CHIhls Photo by Unknown Author ts licensed undcr CCAL-C CEN Ho ch Hs Ch, DixPheto by Unknown Author is IlcensedHHzNCOOHHeleine
Classly Uie TOlOWIg amio acias On the Dasics 0f thenr side group-Polar; nonpolar; positively or negatively charged: Thls Photo Unknown Author Is oh C, Ch; Ho HiN _CH Ihls Photo by Unknown Author ts licensed undcr CCAL- C CEN Ho ch Hs Ch, DixPheto by Unknown Author is Ilcensed H HzN COOH H eleine...
4 answers
(c) Find the velocity of the object at t = 1.Find & parametrization for the tangent line to trajectory c(t) at time t = 1,
(c) Find the velocity of the object at t = 1. Find & parametrization for the tangent line to trajectory c(t) at time t = 1,...
5 answers
WdlMLI 0i loelcar |ravcun] $ GmMrs DeT ha b epon dry dx bvolccJe amolnt ConulHunieamJuvaro 7nornoi Iu Top CnV'Senndvolan
Wdl MLI 0i loel car |ravcun] $ GmMrs DeT ha b epon dry dx bvolccJe amolnt Conul Hunieam Juvaro 7 nornoi Iu Top CnV 'Senndvolan...
5 answers
Fonmalize the following sentences:Let' $ consider propositional language where eans ~Paola happy" .Means Paola paints picture" ,means "Renzo happy" .Formalize the following sentences:"# Pzola is happv and panbs picture then Renzo in t happy" ~if Paola happy, then she paints picture" "Paola happy only if she Peints pictureConstruct truth tables Ior the compound statements(p Vt) + (4 Vt)(p^-pP)7(qAr)
Fonmalize the following sentences: Let' $ consider propositional language where eans ~Paola happy" . Means Paola paints picture" , means "Renzo happy" . Formalize the following sentences: "# Pzola is happv and panbs picture then Renzo in t happy" ~if Paola happy, t...
4 answers
Consider the function f(x) = and the data (2,0.25),(3,0.167), (4,0.125) 2x 1) Find Lagrange interpolating polynomial pz(x) . (Don't simplify) 2) Find Newton interpolating polynomial pz (x) . (Don't simplify) 3) Find an upper bound for the error above
Consider the function f(x) = and the data (2,0.25),(3,0.167), (4,0.125) 2x 1) Find Lagrange interpolating polynomial pz(x) . (Don't simplify) 2) Find Newton interpolating polynomial pz (x) . (Don't simplify) 3) Find an upper bound for the error above...
5 answers
Given the function g(x) shown here, sketch the graph of the derivative function 9' (*) [4 pts]g6)
Given the function g(x) shown here, sketch the graph of the derivative function 9' (*) [4 pts] g6)...
5 answers
Matrix and Solve fhe Sstem Ueing Lhree IOU) Operation to convert the 4o redce roulechelon form5xt3y= + ExA-
matrix and Solve fhe Sstem Ueing Lhree IOU) Operation to convert the 4o redce roulechelon form 5xt3y= + ExA-...

-- 0.021432--