Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
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Was wondering if someone could help me out with this Problem.
It says if Eo and Ho are the peak amplitudes of the E and H fields explain why S
1\2)EoHo where S is the average poynting vector.
And the second part Estimate Eo and Ho;
3m from a 150W lamp
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I'm not sure I understand your notation.
Poynting's theorem is the work-energy theorem of electrodynamics: the work done on the charges by the force is equal to the decrease in energy stored within the field.
The Poynting vector (S) is the energy per time, per area transported by the fields (sort of a flux of energy).
For your second question, I'm assuming a radius of 3 meters from a 100 W lamp is what you are referring to. In this case:
Radial symmetry and all, the integral becomes very simple.
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i think your equal sign plus bracket came out as a smiley !
the first part you need to remember the E and H fields are in phase and are oscillating very rapidly and you need to do a TIME AVERAGE ,,,, you should know the average of a sin or a cosine is one half (1/2) .... (also S=ExH .. you dont need involve B nor magnetic permeability of free space u=u(0) just yet)
the second part you dont need any integrations if you remember the surface area of a sphere is 4 pi times r squared (A=4pi r**2) then remember your S above is the energy per unit area. That 150 watts (joule per sec) is spread out over that area... you gotta divide to get S. But you will then need to know that for a plane EM wave that E is proportional to H.... and we need the proportionality constant.
Maxwell gives curl E = d B/dt ... for plane wave E=E(0) sin(wt-kx) where w=2 pi f and k = 2 pi /l
and B=B(0)sin(...) there are equal but irrelevant phases too.
Now d/dt brings down a factor w, while curl E must go like d/dx bringing down factor k
so Maxwell shows that kE=wB .... ie. E = c B where c=w/k=f.l
Now in terms of H recall B=uH (or u=u(0) if you prefer). Recall c squared equals 1/(ue) where e = electric permittivity of free space and we are there.
thus E=cuH =Z.H where Z = cu=u/sqroot(ue) = sqroot (u/e) is called the impedance of free space.
you will need numerical values of u and e to calculate the E, H fields from energy S.
I DIDNT DO THIS STUFF FOR YEARS ... YOU MUST WORK IT THROUGH NOW AND CHECK. good luck, ask again if still stuck.
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