# B Electrical force vs Gravitational force

#### Jimmy87

Hi,

I have always held (and still do I suppose) the view that gravity is much weaker than the coulomb electrical force due to the fact the equations are so similar you can just compare the constants from each equation showing that the graviational force is many orders of magnitude smaller. However, I stumbled across this article:

https://www.huffingtonpost.com/victor-stenger/myths-of-physics-2-gravit_b_5718233.html?guccounter=1&guce_referrer_us=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_cs=7MJu0LXxQHK4xhEPxWWHIA

What are peoples views on this? Is everything outlined in this true? It seems to say that since Newton's Gravitational constant is not dimensionless you can't compare the strengths as I outlined at the start of this thread? I kind of get the point they are making because you could come up with a compatible equation for gravity with different units that makes the constant of proportionality much bigger. However, I thought that since both equations use Newton's and square meters they are directly comparable?

Thanks!

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#### sophiecentaur

Gold Member
Unfortunately the site tells me that my cookies are disabled but they are not disabled in Safari.
Newton's Gravitational constant is not dimensionless you can't compare the strengths as I outlined at the start of this thread
You can compare the Forces involved when the Masses and Charges are of the orders of magnitude that we encounter in Our World and you get a massive ratio. The Coulomb and the kg are the units that we use and you could say that they are 'unreasonable' quantities except that they are extremely convenient in most respects.

#### Jimmy87

Unfortunately the site tells me that my cookies are disabled but they are not disabled in Safari.

You can compare the Forces involved when the Masses and Charges are of the orders of magnitude that we encounter in Our World and you get a massive ratio. The Coulomb and the kg are the units that we use and you could say that they are 'unreasonable' quantities except that they are extremely convenient in most respects.
I have copied and pasted it all:

Victor Stenger, Contributor
Physicist, PhD, bestselling author
Myths of Physics: 2. Gravity Is Much Weaker Than Electromagnetism
08/26/2014 05:19 pm ET Updated Oct 26, 2014

This is one you will hear in physics classrooms and read in physics textbooks. It even seems to be familiar experience. The magnetic repulsion between the like poles of two small bar magnets easily overcomes their mutual gravitational attraction.

But the sun and Earth have magnetic fields too, and their mutual gravitational attraction easily overcomes their magnetic interaction. When Newton derived Kepler’s laws of planetary motion he just needed his law of gravity and did not have to take into account the magnetic and electric fields of the sun and planets.

So it’s not so obvious. Electromagnetism dominates at the atomic and subatomic levels. But on the planetary level it’s the other way around.

The magnetic force results from electric currents that are moving electric charges. It is part of the same phenomenon as static electricity, referred to as electromagnetism. If you are in a reference frame in which a charge is at rest, you see electricity. If you are in a reference frame in which a charge is moving, you see magnetism.

The static electric force between two charged bodies is given by Coulomb’s law, which says that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

The gravitational force between two particles is given by Newton’s law of gravity, which says that the force between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between them.

The electric and gravitational force laws are both inverse square laws, so if one computes the ratio of the forces between two bodies, the distances cancel. For the electron and proton, the gravitational force is 39 orders of magnitude weaker than the electrical force. This is the source of the myth that gravity is a much weaker force than electromagnetism.

Why base our estimate of the relative strength of gravity and electromagnetism on these two particular particles? The proton is not even elementary but composed of quarks.

In fact, there is no universal way we can specify the absolute strength of the gravitational force. Newton’s gravitational constant G is not dimensionless and so is not a good measure of the strength of gravity since it depends on what units you use.

The absolute strength of the electromagnetic force is specified by a dimensionless parameter alpha called, for historical reasons, the fine structure constant. It is actually not a constant but varies with energy. However that variation is very gradual and for most practical purposes alpha can be taken to have a value of 1/137.

Conventionally a dimensionless parameter alpha-G is defined to represent the gravitational force strength. It is proportional to the square of the proton mass and has a value 23 orders of magnitude less than alpha. So “officially,” gravity is this much weaker than electromagnetism.

However, as we have already noted, the proton is not even a fundamental particle so it makes no sense to use it to define the strength of gravity. The only natural mass that can be formed from the basic constants of physics is the Planck mass, which is macroscopically large. It is about 22 micrograms, whereas a speck of dust is only about 1 microgram. If you define the dimensionless strength of gravity using the Planck mass you get exactly 1. In the case, gravity is 137 times stronger than electromagnetism.

Gravity is so weak at the atomic and subatomic level because the masses of atoms and subatomic particles are so small. It is strong on the planetary scale because the masses of planets are so large.

However, a good question is: Why are the masses of elementary particles so small compared to the Planck mass? This is a major puzzle called the hierarchy problem that physicists have still not solved. However, it is to be noted that, in the standard model, all elementary particle masses are intrinsically zero and their masses are small corrections resulting from the Higgs mechanism and other processes. The hierarchy problem can be recast to ask why the corrections are not on the order of the Planck mass.

The lack of an absolute strength of gravity does not mean that its strength relative to the other forces is not important. Changing the definition of the strength parameter does not change the ratio of the forces between two bodies in any specific situation. But, the point is, that ratio is not the same in all cases. In fact, it can be almost anything, depending on the masses and charges of the bodies being compared. In short, it makes no sense to even ask what is the relative strength of gravity and electromagnetism.

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#### sophiecentaur

Gold Member
I have copied and pasted it all:
Thanks.
He is not saying anything out of the ordinary, I think but I am not sure he's making particularly relevant statements for discussions at an everyday level;
For the electron and proton, the gravitational force is 39 orders of magnitude weaker than the electrical force. This is the source of the myth that gravity is a much weaker force than electromagnetism.
Why does he say it's a Myth, I wonder?
It is true that the Coulomb and the kg are arbitrary - which is why he goes into the planck mass etc. And his point implies that it's the electron charge that's the fundamental one. Using different units, the ratio of the forces becomes different. We're in the same neck of the woods where c=1.

Afaics, the reason that gravity dominates in astronomical situations is because the net charge on any object in space is always near zero - positive charges cancel out negative charges. The odd few Coulombs of imbalance on any body in space is not enough to affect any other bodies. But Gravity operates between every object and every other object - it goes on 'for ever' and doesn't cancel out. If you had two planets with enough net charge on each, the Electric Force could beat the gravitational force. It just doesn't happen because they would discharge to a low value.

#### Jimmy87

Thanks.
He is not saying anything out of the ordinary, I think but I am not sure he's making particularly relevant statements for discussions at an everyday level;

Why does he say it's a Myth, I wonder?
It is true that the Coulomb and the kg are arbitrary - which is why he goes into the planck mass etc. And his point implies that it's the electron charge that's the fundamental one. Using different units, the ratio of the forces becomes different. We're in the same neck of the woods where c=1.

Afaics, the reason that gravity dominates in astronomical situations is because the net charge on any object in space is always near zero - positive charges cancel out negative charges. The odd few Coulombs of imbalance on any body in space is not enough to affect any other bodies. But Gravity operates between every object and every other object - it goes on 'for ever' and doesn't cancel out. If you had two planets with enough net charge on each, the Electric Force could beat the gravitational force. It just doesn't happen because they would discharge to a low value.
Thank you for your insights - this has helped. The main point I still don’t get is - is gravity weaker? Using Coulombs and kilograms it is enormously weaker. However, if we use fundamental particles and dimensionless constant then this guy seems to suggest there isn’t much between them?

#### DennisN

Thank you for your insights - this has helped. The main point I still don’t get is - is gravity weaker? Using Coulombs and kilograms it is enormously weaker. However, if we use fundamental particles and dimensionless constant then this guy seems to suggest there isn’t much between them?
I think it is fair to say that under "normal" (usual to us) conditions gravity is weaker than electromagnetism. Or maybe a better way to put it is that the effects of gravity is not as significant as the effects of electromagnetism*.

I think a good basic example is to take two particles, let's say two protons (or two electrons), and calculate (1) the repulsive forces between them due to electromagnetism and compare those with (2) the attractive forces between them due to gravitational attraction. Since both types of force are in Newton (N), they can be compared, and this would show just how weak gravity is compared to electromagnetism; the effect of gravitational attraction in this case is negligible.

* Edit: Unless we for instance take our own bodies as examples and consider the fact that we are continously stuck to Earth due to gravity.

Edit 2: But on the other hand, the reason why our bodies, the molecules and atoms in them, are held together are due to electromagnetism, so this effect could in this case also be seen as rather significant.

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#### sophiecentaur

Gold Member
The main point I still don’t get is - is gravity weaker
The message from this thread is that 'it depends'.
In practice and in the large scale, the electric forces mostly cancel out but the gravitational forces don't - but that is not to do with strength but with the signs of charges. We experience gravity as being a lot weaker but it's not the whole story.
The paper you refer to points out that the basic units of mass and charge that are chosen make all the difference but that, using the 'most' basic units, the gravitational force can be looked upon as 'stronger'.

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