Why Does the Inverse-Square Law Fail at Distances Less Than One Meter?

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SUMMARY

The discussion centers on the application of the inverse-square law (I = P / 4πr²) in calculating radiation intensity at distances less than one meter from a radiation source. Users noted that applying this law at such close distances yields readings that exceed the actual intensity of the source, leading to inaccuracies. The confusion arises from misunderstanding the mathematical implications of squaring values less than one. Ultimately, the participant resolved their query independently, indicating that the formula remains valid across all non-zero distances.

PREREQUISITES
  • Understanding of the inverse-square law in physics
  • Basic mathematical skills, particularly in squaring numbers
  • Familiarity with radiation intensity concepts
  • Knowledge of point source radiation characteristics
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  • Research the mathematical principles behind the inverse-square law
  • Learn about radiation intensity measurement techniques
  • Explore methods for correcting intensity calculations at close distances
  • Study the characteristics of point sources in radiation physics
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This discussion is beneficial for physics students, radiation safety professionals, and anyone involved in measuring or calculating radiation intensity, particularly at short distances from a source.

TreeScience
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I am trying to work out radiation intensity at points along a transect with an increasing distance from the source. Despite having virtually no high school maths, I understand that by applying the inverse-square law (I = P / 4\pir2) to points < 1m from my radiation source is going to give readings which are higher than the intensity of the emitting object, and therefore false.

The embarrassing part is that a) I don't fully understand WHY this is the case and b) I'm not sure how to correct for it. I still need to calculate the radiation intensity at 0.1, 0.25, 0.5 and 0.75m away from the target source. Is there a simple way of correcting it?

This may seem obvious to everyone else, but unfortunately not to me.
 
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The point source is characterized by its power. What do you call "intensity of the source"?
The formula works for all non-zero distances. The radius r=1 does no have any special meaning. I don't see how you come to think that this value (or values less than 1) may be a problem.
 
It was just a question about squaring numbers that are less than one. I didn't mean that the radius was inherently special. Don't worry about it, I've figured it out myself now.
 

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