Inverse Square Law: What & How to Prove It

In summary, the inverse square law states that the force from a point source decreases as 1/r^2 where r is the distance from the source. This can be proven by measuring the force and observing the decrease as distance increases. However, some forces do not follow this law. For the geometric inverse square law, it can be proven using geometry by increasing the area facing the source. Empirical evidence can also be used to prove it, such as measuring the Coulombic force between two charged objects at varying distances.
  • #1
eddybob123
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What is the inverse square law and how do you prove it?
 
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  • #2
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?
 
  • #3
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.
 
  • #4
are you sure? because human measurements can't really prove it
 
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  • #5
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.
 
  • #6
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.
 

1. What is the Inverse Square Law?

The Inverse Square Law is a scientific principle that states that the intensity of a physical quantity, such as light or sound, is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the intensity decreases at a proportional rate.

2. How is the Inverse Square Law applied?

The Inverse Square Law is commonly applied in various fields of science and engineering, such as physics, astronomy, and acoustics. It is used to calculate the intensity of radiation, sound or light at different distances from the source. It is also used in designing experiments and equipment, such as telescopes and microphones, to ensure accurate measurements.

3. Can the Inverse Square Law be proven?

Yes, the Inverse Square Law can be proven through mathematical and experimental methods. The mathematical proof involves using calculus to derive the inverse square relationship between intensity and distance. The experimental proof involves measuring the intensity of a physical quantity at different distances from the source and observing how it follows the inverse square relationship.

4. What are the limitations of the Inverse Square Law?

The Inverse Square Law is an idealized concept and has some limitations in real-world situations. It assumes that the source of the physical quantity is a point source, and that there are no obstructions or reflections between the source and the measuring point. In reality, sources are not point sources, and there can be obstacles or other factors that can affect the intensity measurements.

5. How is the Inverse Square Law related to the law of gravity?

The Inverse Square Law is closely related to the law of gravity, as both follow the same mathematical relationship. The law of gravity states that the force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases at the same rate as the intensity of a physical quantity decreases with distance according to the Inverse Square Law.

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