# Inverse square law conundrum

• joeyjo100
At a small but nonzero distance, the force is not infinite; just a lot larger than it is at larger distances.

#### joeyjo100

We all know the equations for inverse square laws, such as force between two masses or between two charged particles. We were told the force is inversely propotional to the distance between the masses or charges, squared.

But what would the force equal if the distance between, say two point charges, was zero ie they are touching. Common sense says there would be no force, as neither will move, but this situation would mean that the force would equal the product of the two charges divided by zero squared. As far as my limited maths knowledge stretches, dividing by zero leads to an undefined number.

What does this then say about the force? Would it eqaul zero as you might expect? Or would it be undefined?

Point charges are imaginary. Two charged objects with real mass cannot occupy the same space, although they could be "touching" each other, with a finite distance between their center of mass and charge.

As the two charges are brought closer together, the electrostatic force between them becomes larger and larger. For hypothetical, classical point charges, it would be impossible to exert enough force to actually make them occupy the same point -- the required force would be infinite.

The inverse square law is a product of using Gauss' law in a 3-dimensional space. At/inside the surface of the object of mass or charge a new formula has to be derived. For spherically symmetric objects of ~uniform density (such as an ideal planet for example) the new field equation becomes linear.

Does this keep the force from becoming infinite at small distances? On the scale of atomic particles i mean.

No, because elementary charge carriers are still point-particles as far as we can tell. In pure classical physics, electrostatic field diverges to infinity at point charge, and that's just the way it is. In quantum physics, fact that vacuum is not just empty space mostly takes care of that.

K^2 said:
No, because elementary charge carriers are still point-particles as far as we can tell. In pure classical physics, electrostatic field diverges to infinity at point charge, and that's just the way it is. In quantum physics, fact that vacuum is not just empty space mostly takes care of that.

What do you mean by the vacuum not being empy space?

Also, if you compare the strength of the attraction of an electron orbiting a proton, the hydrogen atom, is that attraction more or less than the two absolute electric charges of the proton and the electron? I guess I'm asking at what distance from a particle is their charge measured as it is?

Drakkith said:
Does this keep the force from becoming infinite at small distances? On the scale of atomic particles i mean.
At a small but nonzero distance, the force is not infinite; just a lot larger than it is at larger distances.

As for the distance equaling zero, the uncertainty principle forbids two charges from having exactly the same location.

Drakkith said:
Also, if you compare the strength of the attraction of an electron orbiting a proton, the hydrogen atom, is that attraction more or less than the two absolute electric charges of the proton and the electron?
This question does not make a whole lot of sense. You can't ask if a force is greater than or less than a charge -- that's like asking if an inch is smaller than an ounce.

The charges on the proton and the electron are always the same value, if that helps.
I guess I'm asking at what distance from a particle is their charge measured as it is?
I don't understand.

Last edited:
Alright, let me put it a better way. Given the electric charge of the proton and electron, what is the force between the two at a distance equal to the average distance of an electron around a proton in a Hydrogen atom?

## 1. What is the inverse square law conundrum?

The inverse square law conundrum is a principle in physics that states the intensity of a physical quantity (such as light, sound, or gravitational force) decreases in proportion to the square of the distance from the source.

## 2. How does the inverse square law conundrum apply to light and sound?

In the case of light and sound, the intensity of these waves decreases as they propagate through space due to the spreading out of the waves over a larger area. This means that the further you are from the source, the less intense the light or sound will be.

## 3. Why is the inverse square law conundrum important?

The inverse square law conundrum is important because it helps us understand and predict the behavior of physical quantities such as light, sound, and gravity. It also allows us to calculate the intensity of these quantities at different distances from the source.

## 4. Can the inverse square law conundrum be applied to all physical quantities?

No, the inverse square law conundrum only applies to quantities that exhibit a wave-like behavior, such as light and sound. It does not apply to all physical quantities.

## 5. How is the inverse square law conundrum used in scientific research?

The inverse square law conundrum is used in a variety of scientific fields, including astronomy, physics, and engineering. It helps scientists understand the behavior of waves and make predictions about the intensity of physical quantities at different distances from the source.