Why all forces are subjected 1/r^2?

  • Thread starter Michael F. Dmitriyev
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In summary, the relationships between forces and their corresponding potentials are nonlinear and depend on the geometry of space. This is evident in the fact that forces are subjected to a 1/r^2 relationship in 3-dimensional space and a cube function in 4-dimensional space. The inverse-square proportionality in electromagnetic forces can be easily visualized through the concept of flux and the density of field lines. This is due to the total number of lines being spread out over a larger surface area as distance increases. Similarly, the strength of gravity is inversely proportional to the surface area of a sphere with radius r. However, this relationship is dependent on the value of G, which has been found to be
  • #1
Michael F. Dmitriyev
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Is it not strange thing that all forces are subjected 1/r^2 but not 1/r?
Why their relationships are nonlinear? It must have the some logical explanation or imaginary picture .
 
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  • #3
Originally posted by russ_watters
Its likely just due to the geometry of space. If space were 4 dimensional, maybe it would be a cube function.
But 3-d already assumes a linear dependence, square dependence and cubic dependence.
 
  • #4
FIrst of all, all forces are NOT inverse square proportional to distance. THe strong nuclear force actually increases with distance (up to a point).

THe E-M force's inverse-square proportionality is easily visualized with teh concept of "flux": Imagine a particle that has a force field around it. Imagnine this force field as lines that radiate from the particle (This is the model of electric field lines, for example). The strength of the force on another particle depends onthe density of the field lines from the first particle.

As you move away from the first particle, the same total number of lines will exist but they will spread further and further apart. As distance increases, the density of the lines gets smaller and smaller. Density is "total number of lines" divided by "the surface area of the sphere with a radius equal to the distance."

Area of a sphere is proportional to the square of the radius, density (and thus strength of the force field) is proportional to the inverse square of the distance.
 
  • #5
Originally posted by Michael F. Dmitriyev
Is it not strange thing that all forces are subjected 1/r^2 but not 1/r?
Why their relationships are nonlinear?
1/r is nonlinear, too.
 
  • #6
Originally posted by Chi Meson
FIrst of all, all forces are NOT inverse square proportional to distance. THe strong nuclear force actually increases with distance (up to a point).

THe E-M force's inverse-square proportionality is easily visualized with teh concept of "flux": Imagine a particle that has a force field around it. Imagnine this force field as lines that radiate from the particle (This is the model of electric field lines, for example). The strength of the force on another particle depends onthe density of the field lines from the first particle.

As you move away from the first particle, the same total number of lines will exist but they will spread further and further apart. As distance increases, the density of the lines gets smaller and smaller. Density is "total number of lines" divided by "the surface area of the sphere with a radius equal to the distance."

Area of a sphere is proportional to the square of the radius, density (and thus strength of the force field) is proportional to the inverse square of the distance.
May be a Gravity force, for example, must be equal to
G (4pi) M1*M2/(4pi)r^2
I.e. a gravity force must be inversely to area of sphere with radius r. Then G is not correct and should be multiplied on 4pi.
 
  • #7


Originally posted by turin
1/r is nonlinear, too.
D'oh - can't believe I missed that.
But 3-d already assumes a linear dependence, square dependence and cubic dependence.
I don't understand what you mean: the diagram I linked shows a square relationship between area and distance in 3d space. That geometric relationship is likely the reason we see square (or inverse square) relationships so often in physical laws.
 
  • #8
Originally posted by Michael F. Dmitriyev
Is it not strange thing that all forces are subjected 1/r^2 but not 1/r?
Why their relationships are nonlinear? It must have the some logical explanation or imaginary picture .

Forces are subject to whatever potential energy function defines them, via a gradient:

[itex]\vec{F} = -\vec{\nabla} U[/itex]

Central potentials (1/r) yield inverse-square forces.

But yes, it actually has to do with the dimensionality of the spaces as well. In fact, in modern theories of large extra dimensions, the Newtonian potential/force is expected to deviate from inverse/inverse-square at submillimeter scales.

moderator edit: fixed TeX
 
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  • #9
Originally posted by Michael F. Dmitriyev
May be a Gravity force, for example, must be equal to
G (4pi) M1*M2/(4pi)r^2
I.e. a gravity force must be inversely to area of sphere with radius r. Then G is not correct and should be multiplied on 4pi.

Similar to the way that the original "Coulomb constant", k, turned out to be a variation of the permeability of free space: k = 1/(4 pi epsilon)
 

1. Why are all forces subjected to 1/r^2?

The inverse square law, which states that the force between two objects is inversely proportional to the square of the distance between them, is a fundamental principle in physics. This law applies to all forces, including gravity, electric forces, and magnetic forces.

2. How does the inverse square law work?

The inverse square law can be mathematically derived from the concept of flux, where the amount of force passing through a given area decreases as the distance from the source increases. This decrease follows a 1/r^2 relationship, hence the name inverse square law.

3. Is the inverse square law always accurate?

In most cases, the inverse square law is an accurate approximation for forces at a distance. However, at extremely small distances, such as within an atom, different laws and principles must be taken into account.

4. What happens if the distance between two objects is not exactly 1/r^2?

If the distance between two objects is not exactly the inverse square of the force, the force will still follow a similar pattern, but it may not be as strong or as predictable. This is why the inverse square law is considered a general principle and not a strict rule.

5. Why is the inverse square law important in understanding the universe?

The inverse square law helps us understand the behavior of many natural phenomena, such as the movement of planets, the strength of electric and magnetic fields, and the behavior of light and other waves. It is a crucial concept in physics and has allowed scientists to make accurate predictions and calculations in various fields of study.

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