Inverse Square Law and various space dimensions

In summary, the Inverse Square Law is a physical principle that describes the relationship between the intensity of a physical quantity and its distance from the source. It applies to all three spatial dimensions and can be applied to various physical quantities such as light, gravity, electric and magnetic forces, and sound intensity. The Inverse Square Law is used in scientific research and calculations to predict the behavior of systems with inverse square relationships. Some real-world examples of this principle include the brightness of a light source, the strength of a gravitational force, and the loudness of a sound.
  • #1
Lapidus
344
11
I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained?

I found this below from here, but could not really understand what's going on:

Green.PNG


Is this some theorem that connects the two integrals (Green's theorem possibly?) in (1.7)?

thanks
 
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  • #2
Lapidus said:
Is this some theorem that connects the two integrals (Green's theorem possibly?) in (1.7)?
The divergence theorem. (Gauss's law)
 

1. What is the Inverse Square Law?

The Inverse Square Law is a physical principle that describes the relationship between the intensity of a physical quantity, such as light or gravity, and the distance from its source. It states that the intensity of a physical quantity is inversely proportional to the square of the distance from its source.

2. How does the Inverse Square Law apply to various space dimensions?

The Inverse Square Law applies to all three spatial dimensions (length, width, and height). This means that as the distance from the source increases, the intensity of the physical quantity decreases in proportion to the square of the distance in each of these dimensions.

3. Can the Inverse Square Law be applied to other physical quantities besides light and gravity?

Yes, the Inverse Square Law can be applied to any physical quantity that follows an inverse square relationship. This includes forces such as electric and magnetic forces, as well as other physical quantities such as sound intensity.

4. How is the Inverse Square Law used in scientific research and calculations?

The Inverse Square Law is used in a variety of scientific fields, including astronomy, physics, and engineering. It is used to calculate the intensity of a physical quantity at different distances from its source and to predict the behavior of systems that involve inverse square relationships.

5. What are some real-world examples of the Inverse Square Law in action?

Some common examples of the Inverse Square Law in action include the brightness of a light source, the strength of a gravitational force, and the loudness of a sound. It is also observed in phenomena such as the spread of heat from a fire and the rate at which a radioactive substance decays.

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