# The Naked Scientists Forum

### Author Topic: the inverse square law  (Read 3852 times)

#### allan marsh

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##### the inverse square law
« on: 22/07/2014 12:47:51 »
the force of gravity and say magnetism varies inversely by the square of the distance of separation
D squared.
Why?
and why if the factor is EXACTLY  D squared, does the force not become infinite at source.

#### PmbPhy

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##### Re: the inverse square law
« Reply #1 on: 22/07/2014 14:48:18 »
the force of gravity and say magnetism varies inversely by the square of the distance of separation
D squared.
Why?
and why if the factor is EXACTLY  D squared, does the force not become infinite at source.
I don't see why if the factor is not D squared that the force does not become infinite at source. E.g. if F = kq1*q2/r^3 then when r = 0 -> F = infinite.

In terms of classical mechanics the force is inverse square by hypothesis. That is we assume that it's true. We then compare it with what we observe in experiments. In quantum electrodynamics and/or field theory it may be something they can deduce. I don't know.

However if the field isn't exactly a 1/r^2 force then the mass of the photon wouldn't be zero. But that can be taken into account in special relativity (SR) and SR would still be valid. Other than the invariance of the speed of light that is.

#### Bill S

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##### Re: the inverse square law
« Reply #2 on: 22/07/2014 22:11:33 »
Quote from: Pete
However if the field isn't exactly a 1/r^2 force then the mass of the photon wouldn't be zero.

Lost!  Could you explain that, please.

#### evan_au

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##### Re: the inverse square law
« Reply #3 on: 22/07/2014 22:30:20 »
Quote
the force of gravity and [electric charge] varies inversely by the square of the distance of separation D squared
A classical description is to consider "lines of force" which come out from a source (a mass or a charge). A small test object placed in this force field will experience a force which is proportional to the density of these lines of force.

These lines of force will spread out radially from an isolated source in space. Since the area of a sphere increases as D2, the density of these lines decreases as 1/D2: the inverse square law.

Quote
why if the factor is EXACTLY  D squared, does the force not become infinite at source
The source object rarely approaches zero radius.
Familiar matter has a density of 1-15 grams/cm2. This makes a measurable mass into a definitely non-zero radius.
• Imposing a large charge on a small-radius sphere is likely to cause corona discharge, which loses the charge. That's why high-voltage sources use large spheres for the electrodes.
• Concentrating a high mass into a small volume will collapse into a black hole, which has a non-zero radius.

Perhaps the most familiar almost-point charge is the proton, which plays a powerful role in chemistry. I have not yet seen reports of production of micro-black holes (although they are theoretical possibility).

Quote
say magnetism
Magnetism does not follow an inverse square law, because it always comes in opposing pairs (North and South)*. The "lines of force" join the North and South poles. This means that there is a degree of cancellation within any sphere, and the strength of a magnetic field decays much faster than 1/D2.

*If you ignore the hypothetical "magnetic monopole".

Quote
why if the factor is EXACTLY  D squared, does the force not become infinite at source
In the far-field, gravity and electric charge follow an inverse-square law.

However, in the near-field, local differences in the density of matter or shape of the electrode can cause changes which do not follow an inverse square law. In particular:
• If you test the electric field inside a spherical metal electrode, the electric field is zero, due to Faraday Shielding
• If you test the gravitational field inside a spherical mass, the gravitational field is lower than immediately outside the sphere, declining to zero at the center.

So rather than increasing to infinity when D=0, the force declines to 0 when D=0.

This has been a classical explanation. Of course, in a quantum world, the concept of zero distance is a bit vague, due to the wave-like properties of all subatomic particles (and even atomic particles).

#### Ilinca Sergiu

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##### Re: the inverse square law
« Reply #4 on: 23/07/2014 06:13:39 »
the force of gravity and say magnetism varies inversely by the square of the distance of separation
D squared.
Why?
and why if the factor is EXACTLY  D squared, does the force not become infinite at source.

Because,

-Electromagnetic wave is a stationary particle (not V=c but V=0) resting in a vacuum.
-The matter is the same particles in a fast intermittent collapsing (implozion) with V=c .
-The quant is the illusion exists only because exists the intermittent collapse (implozion) of the matter system of reference in which measurement is done.
-Gravity is an acceleration from intermittent collapsing (implozion) of the matter.

#### alancalverd

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##### Re: the inverse square law
« Reply #5 on: 23/07/2014 07:35:29 »
The inverse square law is

F = G m1m2/r2

Now for a classical spherical body, m = 4 D π r3/3 where D is the density of the material

Therefore as r decreases, so does m, and F decreases more rapidly than 1/r2 if r is contiguous with the surface of the body

So the gravitational force at a classical point is zero.

It is unwise to mix classical and quantum mechanics. It works for proton spin resonance but little else.

#### allan marsh

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##### Re: the inverse square law
« Reply #6 on: 23/07/2014 11:51:15 »
Thanks I now understand the obvious  in classical but quantum is giving me thought
Thanks

#### evan_au

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##### Re: the inverse square law
« Reply #7 on: 23/07/2014 11:52:14 »
Quote
why if the factor is EXACTLY  D squared, does the force not become infinite at source?
This question assumes that it is possible to take two stationary objects which are very close together, and measure their positions with great precision.
Heisenberg's uncertainty principle suggests that this measurement will be a futile exercise.

#### PmbPhy

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##### Re: the inverse square law
« Reply #8 on: 23/07/2014 20:59:02 »
Quote from: Pete
However if the field isn't exactly a 1/r^2 force then the mass of the photon wouldn't be zero.

Lost!  Could you explain that, please.
There's something called a Proca Lagrangian density. See http://en.wikipedia.org/wiki/Proca_action

That website isn't that great. It doesn't tell you that the m in the Lagrangian density is the photons proper mass.

Its a general Lagrangian that one uses to derive the most general form of Maxwell's equations. If you want to see how it's done with the regular Lagrangian density see my website at http://home.comcast.net/~peter.m.brown/em/lagrangian_density.htm

One of the factors in that Lagrangian is the mass of the photon. If the mass is set to zero when you can use that Lagrangian to derive the 1/r^2 law. If the photon mass is not zero then when you use it to derive Coulomb's law then its not an inverse square law.

#### The Naked Scientists Forum

##### Re: the inverse square law
« Reply #8 on: 23/07/2014 20:59:02 »