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Author Topic: Why does the inverse square law apply so often?  (Read 3272 times)

Offline dentstudent

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Why does the inverse square law apply so often?
« on: 11/12/2008 14:38:58 »
I'm assuming that this is one of those "universal constants", but if not, it seems to appear with great regularity - gravity, drag etc.

What is it about this relationship that makes it so important and frequent in natural science?

(I suspect that if I could answer this, I'd be devilishly clever and rich!)


 

blakestyger

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Why does the inverse square law apply so often?
« Reply #1 on: 11/12/2008 16:53:22 »
Because it's a law - but only, it seems, when the flux lines from a point source are straight. It may not hold if they curve. Others may be able to explain more comprehensively.
 

lyner

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Why does the inverse square law apply so often?
« Reply #2 on: 11/12/2008 17:45:04 »
It's to do with Geometry.
If something, (gravitational field, heat energy, sound etc) is radiating equally in all directions and you draw a sphere around the source, the amount of this thing flowing through a square metre of the sphere (the flux density)  will be equal to the total flux from the source divided by the area of the sphere (assuming it is spread evenly).
The area of the sphere is  4πr2, so the density of the flux will be  1/4πr2. The r2 is on the bottom of the formula so it is proportional to one over r squared: The 'inverse square' law.
The argument also applies when the spread is not symmetrical or when you are just concerned with a particular direction; the 'flux density' is still proportional to 1/r2 .
Over large distances, we believe that space is not truly uniform (Euclidian or like a 3D graph) , the the inverse square law will not apply exactly. Gravity can bend space and cause a lensing effect on the light from distant objects. This can be looked upon as failure of the inverse square law.
 

Offline lightarrow

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Why does the inverse square law apply so often?
« Reply #3 on: 11/12/2008 20:06:03 »
Just to add a little thing to what sophiecentaur said: that law is the result of the field's flux conservation; in the case of EM field, it means charge conservation.
 

Offline LeeE

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Why does the inverse square law apply so often?
« Reply #4 on: 12/12/2008 01:43:32 »
As Sophiecentaur says, it's down to geometry but also, as Blakestyger says, it depends upon the geometry being flat.  For example, the angles within a triangle plotted in a flat geometery add up to 180 degrees but plot a triangle on the curved geometry of a sphere and the angles will always add up to > 180 degrees.
 

Offline dentstudent

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Why does the inverse square law apply so often?
« Reply #5 on: 12/12/2008 07:40:07 »
All excellent answers! Thankyou!
 

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Why does the inverse square law apply so often?
« Reply #5 on: 12/12/2008 07:40:07 »

 

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