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What is the reason for the square attenuation? 
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#1
Mar1913, 12:01 PM

P: 103

I have seen this concept in many places like electrical field, gravitational field, brightness from a distant star or in satellite communication. That is, they seem to be inversely proportional to the square of the distance from the source of that field. What's the reason behind it?



#2
Mar1913, 12:30 PM

P: 824

Conservation of energy. When something like sound radiates in all directions and you draw two balls around it  an inner one and an outer one all the sound that passes through the outer ball must have passed through the inner ball before. But the surface area of the balls increases quadratically with radius, so the intensity (the energy per area) must drop as the square of the radius. The law simply states that the energy spreads out and does not get lost.



#3
Mar1913, 12:37 PM

P: 103

Oh thanks. Simple yet it didn't strike me.



#4
Mar1913, 12:53 PM

P: 1,043

What is the reason for the square attenuation?
The same thinking can clue you in to other geometries. Consider the infinite cylinder. In this case field lines can only diverge in one direction, not in two. So with this geometry we get a 1/r dependence. Consider the infinite sheet. In this case field lines cannot diverge in any direction. Here we get no drop off with distance.



#5
Mar1913, 02:13 PM

P: 210

It is known as the inverse square law and is a characteristic of radiation from a point source with no absorption.
It would not be true for light from a distant star if the light could be absorbed by dust in space. It also applies to the force of gravity as distance increases from a planet. 


#6
Mar1913, 06:13 PM

P: 132




#7
Mar1913, 06:21 PM

Sci Advisor
PF Gold
P: 11,875

If the Maths is not to your taste, then the image in this link says it all, I think. (About half way down)



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