# Relative strengths of the fundamental forces

If I took one mole of electrons, and one mole of protons, confined each to a 1cm[sup]2[/sup] space, and placed them one meter apart, how strong would the attractive force between them be? I’m trying to figure out a way to explain the relative strengths of the basic forces to an intelligent grade-schooler. I know Feynman said something like 30 million tons in one of his lectures, but he used more vague terms like ‘a sugar cube of positive charge and a sugar cube of negative charge on opposites sides of the room,’ or something to that effect. I want to state it more precisely.

8.4 x 10[sup]19[/sup] Newtons. Order of magnitude, you’re talking about the weight of an asteroid if it was sitting on Earth’s surface. This is a stupidly large force — kind of hard to visualize, because of its magnitude. You might want to tone down the magnitude of the charges or place them further apart.

(Also, you would need on the order of magnitude of 10[sup]21[/sup] Joules to get each of these charges compacted into a cubic centimeter of space. This is on the order of the total world annual energy consumption.)

The charge of a mole of electrons (and protons) is called the Faraday constant, and is approx 9.610[sup]4[/sup] C. Coulomb’s constant is about 9.010[sup]9[/sup] Nm[sup]2[/sup]C[sup]-2[/sup].

So the coulomb force between two “mole charges” one metre apart is: 9.010[sup]9[/sup] * ( 9.610[sup]4[/sup] )[sup]2[/sup]) / 1[sup]2[/sup] = 8.3*10[sup]19[/sup] N, which is a lot.

9.43 quadrillion tons?!? Holy crap! Did I do the math right? :eek:

Here’s what GNU units gives me:

``````
You have: (8.4e19 N)/gravity
You want: ton
(8.4e19 N)/gravity = 9.4419756e+15 ton
(8.4e19 N)/gravity = (1 / 1.0591004e-16) ton

``````

So, yeah, that sounds about right.

I often hear it stated this way, which I think would be effective for what you want to do:

The electrostatic forces between the electrons in your feet and the electrons in the floor are strong enough to overcome the force of gravity exerted by the entire earth. Gravity is incredibly weak compared to the other force(s).

1.41 times the mass of 45 Eugenia, an asteroid over 200 kilometers in diameter. Egads.

1 = stong numclea force

10^-3 = electromagnetic force

10^-16 = weak nuclear force

10^-41 gravity

cite

Something like 1/10[sup]40[/sup] the strength of the electromagnetic force, IIRC. colonial correctly (and more precisely) beat me to it.

Not sure where I got the “numclea” force from, though.

I’ve never quite understood what this means. Consider two protons one meter apart and two electrons one meter apart. Since the mass of a proton is roughly 1000 times the mass of an electron, the gravitation attraction between two protons will the one million times stronger than that between two electrons while the electrostatic repulsion will be equal. So if the electrostatic force is 10^-38 times weaker for electrons it’s only 10^-32 times weaker for protons. Therefore, as those numbers aren’t qualified in any way, this can’t be what they mean.

And since the nuclear forces vary differently with difference than gravity and electromagnetic, I have no idea how those comparisons are even made.

What do they mean?

Can I get that figure in stalnakes?

I think they’re just comparing the size of the constants in the equations. Here’s a pagethat actually discusses the assumption made in making the comparisons. They come up with slightly different results than the previous cite, but with an order of magnitude or two.

You’re right on this point; you have to specify for which particles you’re comparing the forces. The usual choice is electrons, since they’re the most common fundamental particle that has charge. (Protons aren’t fundamental particles, since they have more fundamental particles—i.e., quarks —inside them.)

This is a point that usually gets glossed over. Roughly speaking, the force between two particles will still vary proportionally to 1/r[sup]2[/sup] so long as the particles are close enough together. The ratio of the constants of proportionality is basically what gets compared in this case. (This is again for a specified set of particles — usually quarks in this case, since leptons don’t interact via the strong force)

Here is another more technical cite which gives ratios different from those posted before.
Posted here are ratios based on the dimensionless coupling constant for each force:

1: strong
1/137: electromagnetic
10^-6: weak
10^-39: gravity

I am not real happy about the discrepancy. Maybe one of the board technical specialists
will show up and provide some clarification.

:smack:. I just now caught this. You guys are slipping—I should have been branded the village idiot by now and the yo’ momma jokes should be flying.

How do we know it’s the force that is stronger? Maybe our units for electric charge are too big?

On the other hand, though, electrons aren’t subject to the strong nuclear force (or the color force, which the strong nuclear force is really just a side effect of) at all. You need to use some sort of hadron to compare the strong force to gravity, and all free hadrons are composite particles.

Could you get precise numbers for all the coefficients if you picked an Up quark and a Down quark (or anti-quark, if that’s better) as your two standard particles? What would those numbers be?

If you’re using individual quarks as your standard particles, then you need to deal with the full color force, not just the strong force. Unfortunately, we know very, very little about the color force: It’s not just a matter of not knowing the coupling constants; we’re not even sure about the functional form. And it might even be something weird like “constant force regardless of distance”, in which case it isn’t really even meaningful to describe it in terms of a coupling constant.

Probably the cleanest option would be to just consider the force between a pair of protons, and handwave away the fact that they’re composite particles.