Why does electromagnetism attenuate so much faster than gravity?

Question

Electromagnetism and gravity are both inverse distance-squared laws, so why is gravity affected so much less by distance?

1. Is it that electrical charges tend to pretty much completely balance out beyond a micro scale?
2. Is it that matter interferes with electromagnetism, while it adds to gravity?

I suspect that #1 is the main reason why electric fields don't matter at macro scales, but it doesn't explain magnetic fields. I assume stars often make magnetic fields like the Earth's. Do those magnetic fields matter at the level of solar systems? Galaxies?

Answer 1

Your first explanation is correct when it comes to electrostatic fields. All macroscopic matter is neutral and therefore there are no possible sources of large electrostatic fields. Furthermore, regarding your second explanation, matter does have an effect on electric fields, particularly on those within it. If you have a perfect conductor and you expose it to an electric field all of the charges on its surface will redistribute such that the charge inside the conductor is zero. On the other hand, if you have a dielectric the electric field polarizes the material. Effectively it pushes the positive charges in one direction and the negative charges in the other, creating a "rival" electric field in the opposite direction to the original one, effectively reducing the strength of the field within the material.

As for magnetic fields, it's illustrative to consider the field produced by a circular current far away from its axis. You can check the NASA article "Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop" for more information. The key point si that the magnetic fields drop off as $1/r^3$, not as $1/r^2$. This makes sense if you consider the multipolar expansion of the magnetic vector potential (equivalent to the multipolar expansion for the scalar potential). Since there is no magnetic charge, the first term of the expansion, the monopolar term, disappears. But this term is what grants electrostatic fields the $1/r^2$ dependence, since it causes potentials $V$ that drop off as $1/r$. Since it does not exist for magnetic fields, necessarily you need to at least go to the dipolar term, which drops off as $1/r^3$.

Also, there just really aren't any current sources that can "stack up" like mass can.

Answer 2

I suppose that on Earth the largest scale at which we see buildup of electrostatic potential is the buildup to lightning strikes.

To build up electrostatic potential requires a physical mechanism that leads to separation of positive and negative charge.

In physics experiments a van de Graaff generator is used to build up a large electrostatic potential. (Named after the physicist Robert Jemison Van de Graaff)

As soon as positive and negative charge start being separated the tendency is to move back toward each other, evening out the difference.

A Van de Graaff generator has two jobs that are each other's opposite: be an insulator, so that existing charge separation is maintained, and provide transportation of charge, against the potential difference.

In the natural circumstances of the Earth it is remarkable that buildup of charge separation, leading to lightning strikes, happens at all.

The next higher up scale is charge separation from one celestial body to another.

It seems very unlikely to me that there could be any form of interplanetary charge separation mechanism.

The solar wind plasma consists mostly of electrons, protons and alpha particles. It seems very implausible to me that any star could possibly build up a surplus of either positive or negative charge.

The electrostatic force is so strong that even a tiny surplus of one or the other would reduce outflow of charge particles of the opposite charge.

While gravitational interaction is far, far weaker than electrostatic interaction: gravitational mass can just keep accumulating.

With gravitational interaction there is no repulsion, only attraction.

Gravitating bodies can just keep accumulating, that is why at solar system scale, and at all bigger scales, the only interaction playing a part is gravitational interaction.

Answer 3

If you know or believe that bulk matter is electrically neutral there will be no monopole fields. Dipole fields fall off as $1/r^3$ once you are farther away than the size of the object.

Fifty years ago one of my professors described the best experiment at the time to show the neutrality of bulk matter. Evidently it was done as a senior project at one of the elite US universities. They made a sphere of aluminum with a rather heavy wall. If you consider it as an acoustic cavity you can compute the frequency of the fundamental mode, which is high pressure at the center and low pressure at the outside, depending on the gas you fill it with. If you install an electrode at the center and drive it at this frequency and matter has a bulk charge the cavity should ring very strongly, so put a microphone on the outside and listen. They heard nothing. When you do a null experiment like this you need to prove you are sensitive to something and measure the sensitivity to get your upper limit. Here it is easy. The next order effect if the matter is neutral is that the electrode will polarize the gas, then drive the molecules in and out based on the dipole. Because the polarization and drive force per polarization are both linear in the voltage of the probe the response goes as the square of the drive. This doubles the frequency, so you cut the driving frequency in half and the cavity rings nicely. More electrons in the gas make a better response, so the cavity was filled with $UF_6$.