# Why is force inversely proportional to distance?

• l-1j-cho
In summary: So the "inverse square law" is something that happens to be true in certain situations, but it may not be a fundamental law.He means the gravitational force.The inverse square law is true in the case of Newtonian gravity and electrostatics because they are based on the conservation of energy. But it is not necessarily true for all forces.
l-1j-cho
Hello all :)

A random guy on the internet proposed the question above. Why is force inversely proportional to the square of distance? And he gave us a hint that this is not a physics problem but a math problem. Could you guys give me a clue?

I really don't think that dimensional analysis nor experimental values are the answer that he is looking for.

Last edited:
Well, it isn't true that forces, in general, are inversely proportional to some squared distance.

And, how some particular force is most accurately represented is a problem within physics, rather than within maths.

Which force do you mean? Gravitational and Electrostatic both do, but magnetic, and the weak/strong interactions don't necessarily.
Think about the inverse square law, and how the geometry of something traveling at a constant speed would disperse when emitted by a point object.

oops my mistake.

He meant gravitational force.

I guess you could argue that since the gravitational field lines go radially inward towards the mass, the density of the field lines would be inversely proportional to the surface over which they are spread over. (And therefore inversely proportional to r^2). And since force is proportional to the density of field lines, the force is inversely proportional to distance squared.
But this argument isn't mathematically or physically solid, it assumes too much. (But it does happen to be true in the case of Newtonian gravity and electrostatics).

BruceW said:
the density of the field lines would be inversely proportional to the surface over which they are spread over.

Then, shoudn't it be inversely proportional to the cube of the distance?
I really don;t know :(

the surface of a sphere is proportional to radius squared, so the field lines per area (through a given sphere) is inversely proportional to radius squared.

oh i get it
thanks

This kind of "why questions" are a bit problematic since science doesn't answer them. Science tries to describe what can be observed as concise as possible and then to make models (or even theories), i.e., finding out the pattern behind the observations, by finding an as small as possible set of fundamental laws to explain as many phenomena as possible.

First of all you have to specify which force you are talking about. Not all forces are inversely proportional to the square (!) of the distance! E.g., the strong force between two nucleons is Yukawa-like, i.e., exponentially falling with distance.

The "reason" behind these laws, i.e., the reason for their specific form, can be traced back to the fundamental symmetries of space-time. The best theory we have about the elementary particles which are the building blocks for all known matter (there's more unknown in the universe than known, but that's another story) is the standard model of elementary particles, which bases on the Minkowski geometry of special-relativistic space-time and its Poincare symmetry. This symmetry governs the possible mathematical forms of field equations, which themselves finally lead to the force laws we observe in nature.

For the electromagnetic force it turns out that it is due to a massless vector field, the electromagnetic field, and in the static case you find Coulomb's Law for the force between two structureless point charges, i.e., a central force falling with the square of the distance between the particles.

It is a mathematical fact that inverse square laws for forces, in Euclidean space imply "conservation of force-area over a simply connected surface enveloping the singularity"

However, there is, as yet, no fundamental reason WHY the quantity "force-area" should be conserved, but it is a very pleasing mathematical property with SOME force models, that happens to be true in a few special cases.

## 1. Why is force inversely proportional to distance?

According to Newton's Law of Universal Gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of attraction between them decreases.

## 2. How does the distance affect the force between two objects?

The force between two objects decreases as the distance between them increases. This is because the gravitational pull between the objects becomes weaker as they move farther apart from each other.

## 3. What is the relationship between force and distance?

The relationship between force and distance is inverse. This means that as one variable increases, the other decreases. In this case, as the distance between two objects increases, the force of attraction between them decreases.

## 4. Why does the force decrease as distance increases?

This is due to the inverse square law, which states that the strength of a force is inversely proportional to the square of the distance between two objects. As the distance between two objects increases, the force between them is spread out over a larger area, resulting in a weaker force.

## 5. How does the inverse square law apply to force and distance?

The inverse square law describes the relationship between force and distance, stating that as the distance between two objects increases, the force between them decreases by the inverse square of the distance. This law is applicable to various forces, such as gravity, electric and magnetic forces, and light.

Replies
11
Views
2K
Replies
7
Views
3K
Replies
5
Views
2K
Replies
9
Views
6K
Replies
14
Views
10K
Replies
4
Views
2K
Replies
1
Views
1K
Replies
4
Views
667
Replies
1
Views
1K
Replies
2
Views
4K