# The Naked Scientists Forum

### Author Topic: How large is the electric field of an electron or proton?  (Read 584 times)

#### jerrygg38

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##### How large is the electric field of an electron or proton?
« on: 22/09/2016 14:12:29 »
How large is the electric field of an electron or proton?
Has scientific theory determined the size of the electric field from a single electron or proton? As I see it, the field is quantized and a certain point will be reached where the electric field from a single electron will no longer exist. As soon as you have many charges, the field will grow. In the same light has any scientist calculated how large the gravitational field is for a single neutron? Again as soon as you add huge numbers of neutron, protons, and electrons, the field will grow accordingly. Has anyone come up with these answers?

#### alancalverd

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##### Re: How large is the electric field of an electron or proton?
« Reply #1 on: 22/09/2016 18:10:57 »
The field is not quantised, and for a free charge, it extends to infinity (though at infinitesimal strength). The behaviour of a test charge at a long distance from the source tends rapidly towards a classical continuum - you can ignore quantum effects once you get more than a few atomic diameters away.

You can calculate the gravitational field for a neutron from the classical equation since its mass is known. If you have lots of neutrons in a small space, you can apply the classical equation to find the gravitational field of a neutron star.

#### syhprum

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##### Re: How large is the electric field of an electron or proton?
« Reply #2 on: 22/09/2016 20:16:53 »
Is it the accepted view that the electric field is not quantized, I do not like to see terms such as infinite and infinitesimal in a scientific discussion.

#### jerrygg38

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##### Re: How large is the electric field of an electron or proton?
« Reply #3 on: 22/09/2016 22:12:10 »
Is it the accepted view that the electric field is not quantized, I do not like to see terms such as infinite and infinitesimal in a scientific discussion.
The problem is that if space is quantized, there will be jumps in the electric and gravitational fields. A point will be reached where for a tiny distance more, the standard equations will not allow another drop in the field. If space was continuous then the fields could be continuous but I am under the impression that space has a minimum distance between jumps and if this is true, the fields must stop.

#### evan_au

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##### Re: How large is the electric field of an electron or proton?
« Reply #4 on: 22/09/2016 22:22:29 »
Quote from: syphrum
Is it the accepted view that the electric field is not quantized?
It is accepted that electric charge is quantized: proton = +1, electron =-1, neutron=0. Quarks have fractional charge: 2/3 or 1/3, but you cannot obtain an isolated quark at anything like normal energies.

As you move away from the quantized charge, the electric field intensity decreases as an inverse square law.

Since distance is not quantized (or, at least, the Plank length is so small that we can't measure it), then the electric field is not quantized.

The rest mass of a proton or electron is quantized, but their relativistic mass is not. The gravitational field is not quantized.

Quote
I do not like to see terms such as infinite and infinitesimal in a scientific discussion.
In formal mathematical terms, you would say "As distance from the proton approaches infinity, the strength of it's electric field asymptotically approaches zero.".

But this is a reasonable shorthand: "for a free charge, the electric field extends to infinity (though at infinitesimal strength)".

#### alancalverd

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##### Re: How large is the electric field of an electron or proton?
« Reply #5 on: 22/09/2016 23:33:30 »
I do not like to see terms such as infinite and infinitesimal in a scientific discussion.

That could seriously limit your participation in scientific discussions! We use a lot of mathematical terms like infinite and infinitesimal to describe things that are not limited.

And whilst the Planck length is the smallest measurable increment of distance, it has no physical reality. A continuum is a continuum.

#### jeffreyH

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##### Re: How large is the electric field of an electron or proton?
« Reply #6 on: 23/09/2016 00:03:37 »
It's as thick as two short Plancks.

#### jerrygg38

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##### Re: How large is the electric field of an electron or proton?
« Reply #7 on: 23/09/2016 00:29:53 »
From this discussion, it seems to me that the issue of the quantization of the electric and gravitational field has not been raised. I am surprised that Plank, Einstein and company has not raised the issue. If we look at a wave in water, it gets smaller and smaller but eventually stops. So it is difficult for me to believe that the electric field reaches to the radius of the universe. Or perhaps at the maximum radius that is where the final step occurs.
Another issue that is possible is that there are levels of charge noise and gravitational noise in the universe. Perhaps the final level of the fields is reached when we reach the ambient noise levels. Has anyone discussed these problems of gravitational and electrostatic noise?

#### evan_au

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##### Re: How large is the electric field of an electron or proton?
« Reply #8 on: 23/09/2016 10:21:37 »
Quote from: jerrygg38
If we look at a wave in water, it gets smaller and smaller but eventually stops.
How do you know that?

Ocean waves still have significant amplitude after thousands of km.
Provided they don't run into shallow water or land, eventually they will get so small that they are smaller than the ripples caused by gentle local breezes.

As you say, the effect of a distant proton is masked by the electric and gravitational fields of nearby objects.

So the range is infinite (or as large as the universe), but at large distances it becomes infinitesimal and insignificant.

#### jerrygg38

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##### Re: How large is the electric field of an electron or proton?
« Reply #9 on: 23/09/2016 14:47:30 »
Quote from: jerrygg38
If we look at a wave in water, it gets smaller and smaller but eventually stops.
How do you know that?

Ocean waves still have significant amplitude after thousands of km.
Provided they don't run into shallow water or land, eventually they will get so small that they are smaller than the ripples caused by gentle local breezes.

As you say, the effect of a distant proton is masked by the electric and gravitational fields of nearby objects.

So the range is infinite (or as large as the universe), but at large distances it becomes infinitesimal and insignificant.
You make good points. It may very well be that the answer is the radius of the universe as measured from every point in the universe. I always look at various alternate possibilities and it is good to see other peoples thoughts.

#### The Naked Scientists Forum

##### Re: How large is the electric field of an electron or proton?
« Reply #9 on: 23/09/2016 14:47:30 »