Nereid, I think that you are both right but incomplete here. and will try to show which is which.
The propagation of
sound energy away from "standard source configurations" is a wave process, and the change in field
electric field strength due to "standard charge configurations" and the
gravity field strength under those configurations are all mathematically identical. That is, if charge or sound sources are distributed equally on one of those "configurations" — a tiny but finite point sphere; an infinite line, or an infinite plane — the strength of the resulting fields at distance r follows the same rules. That is, as you point out, 1/r² for a "point" source; 1/r if the source is a long line, and constant if the source is the infinite plane. neglecting the peculiar case in acoustics where a source can have directionality, r's exponent will range continuously from zero to 2. (This also rules out things like dust extinction for light, to keep it simple.) [references:
Noise and Vibration Control Engineering, Beranek and Vér, John Wiley & Sons, 1992; and
Electromagnetics, 2d Ed., Joseph Edminster, Schaum's Outline Series, McGraw Hill, 1993.
For cases where the source may not be an exact small point, or may be a less than infinite line, or a planar source of limited dimensions, the exponent is a "decimal" number somewhere between the three integer exponents. That means the field strength is decreasing with increasing distance at a rate somewhere between two of the standard cases. The acoustical case uses equations which, in a sense, say, "this finite square (or rectangle or circle) source will fall off slowly at first if you are "real close" to it (its distributed sources subtend a wide "field of view" to the observer or receiver), but as distance increases, all shapes collapse until, with enough distance, they are all point sources at the limit. Stars are almost all at this limit due to their great distance from us, for example, and in open space their light intensity (and gravitational force) fall off in proportion to 1/r², as advertised, and as you correctly point out.
But in cases where there are relatively large or "bulk collections" of particles, and a fraction of those particles are ionized and separated so that there also negative and positive electromagnetic forces in play, the situation may (not always!) be dominated by the electromagnetic forces, and in particular it is not a simple electrostatic situation, but more an electrodynamic that, it turns out, is going on.
I started to look at an arrangement of particles in a Maxwellian velocity distribution to compare average forces among charged and uncharged particles to compare gravity vectors to EM force vectors etc. but that's the complicated, long and correct way to do it. If you have a line source (call it case=infinite) of gravity "charges", outside the line the gravity field is related to distance r from the normal to the axis to the remote (neutral or charged) particle as 1/r, using Newton's well-known "force between 2 masses" gravity equation. On the other hand, the attraction or repulsion of a charged particle in the field due to a linear distribution of the separated charges in the infinite line will be controlled by how many and the distribution of charge along the line. Assuming it is equally distributed, just like the gravity distribution, along the line, then the EM forces between the line of charges and the
test charge at distance r will also be in a 1/r relationship, but the strength from charged particles is reduced by the number of charged particles in the line source (the fraction of ionization) and increased by the difference in strength between the gravity force and the EM force, to begin with.
So what dominates? Say you have a line source constituted of only hydrogen atoms (the simple model) and one atom out of every, say, 1000 atoms has been ionized to produce two separated charges. Electrostatically, you can guess that the whole line should appear net neutral to the test particle at r, because there are equal numbers of positive and negative charges attracting and repelling.
But there
are other forces at work. You might say that nothing in space is static. If it were, all the gravity vectors on those "motionless" particles, charged or not, constituting the line would act toward the center of gravity of the line, which is right at the center, and they would all pull themselves together into as small a clump of matter as possible. If the atoms and charged particles have random thermal motion, however, then a kinetic gas pressure exists, and in the nature of gas, the agglomeration would try to equalize its pressure with that of the surrounding medium — i.e., the tenuous interplanetary or interstellar medium, and despite gravity the particles, due to a decreasing number of collisions and an increasing mean free path between collisions would eventually drift farther and farther apart and cool and become less and less influenced by each other.
Also within the line source region, unless ionization conditions remained, under thermal collisions and radiation, the charged particles would over time tend back toward a neutral condition, and join the march toward diffusion.
Observations show that there are magnetic fields in plasma filaments, however. There
are therefore moving charges, or electric currents, in those filaments. (They are not, so far as we have determined, filaments constituted of a whole lot of little bar magnets all oriented nose to tail.
)
Current flows generate magnetic fields, and charged particles generate electric fields. That these are complex goes almost without saying: Langmuir called it "plasma" for a reason - it's as if its movement and behaviour were "alive" in its complexity. It is a huge system of feedback loops and interactions at various distances, with change and instability almost the only constant, albeit it very slowly over cosmic dimensions. In space plasmas, Paul Bellan [
Fundamentals of Plasma Physics, Cambridge University Press, 2006] writes,
Most of the astrophysical plasmas that have been investigated have temperatures in the range of 1—100 eV and these plasmas are usually fully ionized... Plasma dynamics is determined by the self-consistent interaction between electromagnetic fields and statistically large numbers of charged particles.
Other writers note that complete ionization is not necessary for matter to exhibit plasma behaviour. In space, with the occasional exception, plasma behaviour
is the rule. Maxwell, Lorentz, Biot-Savart, Vlasov, Debye, Alfvén, Landau, Bernstein, Rayleigh-Taylor, Fokker-Planck, Manley-Rowe, and Brillouin are some of the names associated with the many rules and laws and morphologies and instabilities and methodologies used in trying to depict plasma behaviour mathematically.
Plasma and plasma behavior are observed and inferred in space; they are observed in labs on Earth, taught in universities and used in a wide variety of construction and industrial processes in applied engineering form. Every single photon (other than reflections) reaching our eyes and instruments from space is generated by electrons in plasma. The richness, diversity and extreme complexity of plasma and the physics of plasma are beyond the scope of an informal, quantitative discussion forum such as this. The more that people can understand or just grasp the mathematical and physical principles involved, the better, of course. This is a recognized science, after all, and it is in its infancy, human pride notwithstanding. We all have a lot to learn, and not much time (individually) in which to learn it.
Sure, 1/r versus 1/r² is interesting and instructive, but where plasma behavior occurs, it is most often irrelevant, because gravity is only
a force, almost always
not the dominant force, in describing plasma behaviour.
Jim
