# Potential/inverse nth power law

• granpa
In summary, the conversation discusses the potential in the center of a solid 3D sphere with uniform mass density and a total mass of m, which is gravitating according to an inverse 10th power law. There is a misconception about the relationship between radius and density, and the use of Gauss' law is mentioned. The potential as a function of radius is also mentioned, and the relevance of 11 dimensions is brought up.
granpa

## Homework Statement

is the potential in the center of a solid 3d sphere having uniform mass density and a total mass of m (which is constant), which is gravitating according to an inverse 10th power law, inversly proportional to the square of its radius? this isn't really homework but I figured people would think it was anyway. (this concerns nuclear forces and potentials). the number 10 has no special significance.

## Homework Equations

potential at point x = energy released in moving from infinty to point x.
energy=force * distance

## The Attempt at a Solution

the calculus is far beyond me but intuition and symmetry tell me that it must be.

obviously the field is negligible everywhere except very close to the surface of the sphere. if the radius is cut in half then the density would be 8 times as great.
so we can think of this as making the field everywhere 8 times as great but halving the distances involved so the potential would be 8/2 times as great.

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That's is so wrong headed in all respects. You said 'uniform density', how does cutting the radius in half increase the density by 8? If you are trying to apply Gauss' law, it only applies to inverse square fields in 3 dimensions. Now it's your turn. Tell me what else is wrong? Why don't you just use calculus?

radius is the variable. mass is constant.I want to know the potential as a function of radius.
half the radius=1/8th the volume. hence 8 times the density. uniform density means that the mass is distributed uniformly throughout the 3 dimensional interior of the sphere.

though I had no thought of using gauss's law nevertheless it is a fact that gauss' law applies to inverse 10th power law in 11 dimensions. you can think of the sphere as being a flat 11 dimensional object. you should be able to see immediatly that (within the 3 dimensions containing the sphere) the field is negligible everywhere except very near the surface of the sphere.

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anybody?

## 1. What is the potential/inverse nth power law?

The potential/inverse nth power law is a mathematical relationship that describes how one variable (the dependent variable) changes in response to changes in another variable (the independent variable). Specifically, it states that the dependent variable is inversely proportional to the nth power of the independent variable.

## 2. What is the significance of the nth power in this law?

The nth power in the potential/inverse nth power law indicates the degree of the relationship between the two variables. For example, if n is 2, the relationship is quadratic, if n is 3, the relationship is cubic, and so on.

## 3. How is the potential/inverse nth power law different from other power laws?

The potential/inverse nth power law is unique because it describes an inverse relationship between the variables, while other power laws describe a direct relationship. In addition, the potential/inverse nth power law includes the exponent n, which allows for a more precise description of the relationship between the variables.

## 4. What are some real-world applications of the potential/inverse nth power law?

The potential/inverse nth power law can be applied in various fields, such as physics, economics, and biology. For example, it can be used to describe the relationship between force and distance in Newton's law of gravitation, the relationship between supply and demand in economics, and the relationship between species diversity and habitat area in ecology.

## 5. How is the potential/inverse nth power law determined or calculated?

The potential/inverse nth power law is determined by plotting the data on a graph and observing the trend. If the relationship appears to be inverse and the data points align in a curved line, then the potential/inverse nth power law may be a good fit. The value of n can then be determined through statistical analysis or by trial and error.

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