Inverse Square Law: What & How to Prove It

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SUMMARY

The inverse square law describes how forces such as electric, magnetic, and gravitational forces diminish with distance from a point source, specifically following the formula 1/r², where r is the distance. This law can be empirically validated through experiments, such as measuring the Coulombic force between charged pith balls at varying distances. The geometric interpretation of the inverse square law can also be demonstrated using geometry, particularly in relation to the area of a sphere. However, it is important to note that not all forces adhere to this law, making empirical validation crucial for specific cases.

PREREQUISITES
  • Understanding of basic physics concepts, particularly forces and fields.
  • Familiarity with Coulomb's Law and electric charge interactions.
  • Knowledge of geometric principles related to area and volume.
  • Basic experimental design and measurement techniques in physics.
NEXT STEPS
  • Study the derivation of Coulomb's Law and its applications in electrostatics.
  • Explore geometric proofs of the inverse square law using area calculations.
  • Investigate other forces that do not follow the inverse square law, such as magnetic forces at close range.
  • Conduct experiments to measure forces and validate the inverse square law empirically.
USEFUL FOR

Students of physics, educators teaching force dynamics, and researchers interested in experimental validation of physical laws will benefit from this discussion.

eddybob123
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What is the inverse square law and how do you prove it?
 
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eddybob123 said:
What is the inverse square law and how do you prove it?

That sounds interesting. What is it? Could you provide a web link or two to help us understand your question?

How do you think something like that could be "proved"? What is the formula for the area of a sphere maybe?
 
For forces like electric, magnetic, and gravitation, the inverse square law says that the force from a point source gets weaker the further you go from the source of the force. It falls off as 1/r^2 where r is the distance you are from the source. You prove it by measuring it. Other things obey the inverse square law too. If you have a light source, then the amount of light landing on a fixed area (like a piece of paper) facing the source will fall off as you move the area further away. It will fall off as 1/r^2. This is the geometric inverse square law. If you have a piece of paper at distance r, and you move it to 2r, you will have to make it 2 squared or four times larger in order for it to look the same size. This kind of inverse square law you can prove with geometry.
 
are you sure? because human measurements can't really prove it
 
Last edited by a moderator:
eddybob123 said:
are u sure? cause human measurements can't really prove it

Some forces do not obey the inverse square law, so for a general force, you can't prove it.

For the geometrical inverse square law, you can prove it, by geometry.
 
eddybob123 said:
are you sure? because human measurements can't really prove it

Course we can prove it empirically. We take two pith balls and give them each a net charge and then measure the Coulombic force as a function of distance. We will see that the force drops off as 1/r^2 with some proportional constant.
 

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