Welcome. So, we have analyze the nature of the fields electric field and magnetic fields radiated by a current element in the last class. Now, we will see that how; what is the proof that radiation is taking place.
So, we look at the expression of Efar-field and Hfar-field at a distance from the antenna these are dominating. So, other fields are negligible there so, we write that now we will have to take the Pointing vector, Pointing vector you know E cross H*. So, we will have to take this in spherical coordinate; that means, ar , aθ and aΦ these all you know just I, if any of you forgot that is why I am writing Er, Eθ, EΦ and Hr*, Hθ*, HΦ*. But you know that in our case, we do not have this.. So, these are 0’s here and you can find this expression.
So, you can find that E cross H* that will be having a radial component. So, this will be the expression, now again if you look at you have all this expressions just look at them Er HΦ*, that actually is a purely imaginary term. So, in the Pointing vector it is present, but we know the time average power density is given by phasor Sav that is half real E cross H*
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So, that only given E time average power flow that is only local power there; So, that is nothing, but only ar so, it has only a radial component that means, time average power is flowing only in the radial direction. It is not flowing in any other direction; that means, I have the current element here, this is my current element in this direction it is going in these direction. So, all radial directions it is flowing out, but in no other direction it is flowing. So, if I look from here it is flowing here, if I look from here, it is flowing here, but do not assume that just because I have drawn arrows means it is equally flowing.
I have said that no real antenna can radiate equally, similarly all direction that will see just now that there is a shape of that, but it is having radiation power is flowing out. So, this is the proof that it is getting radiated.
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