Talk:Coulomb's law

Am I correct in translating my physics book's ambiguous claim that the "charges must be small" as meaning the two objects must have small volume?

Even if this is correct, can someone clarify what "small volume" means? On one hand, the implication seems to be, the smaller the volume of the two substances/objects/particles, the more correctly the Law will predict the forces acting on them. So perhaps we could reformulate Coulomb's Law as a statement along the lines of "as the limit of the particles' volumes goes to 0..." But if this is so, how are we to think about the lowest levels of matter, where everything seems to be quantized, not continuous?

Finally, I don't suppose there's a handy expression for how accurate one can expect Coulomb's Law (or other such laws) to be, given the size of the substances involved? How does the day-to-day engineering question of "Is Coulomb's Law accurate enough for my particular use?" get answered? (Or perhaps Coulomb's law, by itself, isn't useful in a day-to-day sense....)

Contents

1 Use of Coulomb's Law 2 Units of coulomb's constant 3 Other article? 4 Symbol for permittivity

Use of Coulomb's Law

You're right. Stictly speaking Coulomb's law is only valid for (unphysical) point particles. For extended shapes you need to treat the object as an infinite number of infinitely small charges. Once you've broken down the shapre this way, integration yields the actual forces on the object. For charged non-conducting spheres, it happens that the Coulomb's law gives exact results.

What I described above is the classical answer, and gives excellent results for volumes that are a few orders larger than atoms, and charges that are a few orders larger than the charge of the electron. Once you want to start talking about very small distances or charges, you get into really awful and messy quantum mechanics.

In typical applications Coulombs law is a very useful approximation. Anytime you're dealing with objects you can hold (even if you need tweezers), and the objects are separated by (say) ten or one hundred times the larger of thier radii, Coulomb's law will give good results. If your objects have reasonably spherical shapes (say cubes, octohedrons, etc...), you'll get good results even closer.

--JeffVaughan 16:38, 29 Sep 2004 (UTC)

Units of coulomb's constant

Unless I'm mistaken, the units for coulombs constant are exactly the opposite of what they should be, i.e. rather than C^2*N^(-1)*m^1, it should be N*C^(-2)*m^(-1).

I don't know about the other units (F m^(-1) or whatever), though, so I'll leave it for the moment. 81.226.53.55

You are obviously right, and the units including farads are inverted as well. I changed it in the constant k, which obviously should have the inverse of the units of ε₀. Was this the only place with the problem? Gene Nygaard 22:53, 16 Feb 2005 (UTC)

i dunno why it was necessary to introduce <math> k \ <math> in place of <math> \frac{1}{4 \pi \epsilon_0} \ <math>, but since it was done, the units on <math> k \ <math> should be the reciprocal of <math> \epsilon_0 \ <math>. in addition, the symbol <math> k \ <math> can be confused by some to be the Boltzmann constant, which is why i don't think it should be there at all. also, Gene, why do you think "esu of charge " is necessary. esu is a unit of charge, synonymous with statcoulomb, although it is dimensionally defined in terms of base cgs units. i don't think the article was improved with the last 2 or 3 edits. r b-j 23:51, 16 Feb 2005 (UTC)

No, "esu" was used to identify any electrostatic unit; there were "esu of charge" and "esu of current" and "esu of induction flux" and "esu of magnetic field intensity" and "esu" of many other things. Gene Nygaard 00:24, 17 Feb 2005 (UTC)

okay, then we should just say statcoulomb for the cgs version of Coulomb's law. r b-j 04:12, 17 Feb 2005 (UTC)

Other article?

What's the relation between this article and Coulomb barrier? Should they at least link to one another? -- Tarquin 12:51, 10 Mar 2005 (UTC)

Symbol for permittivity

Rbj, why do you put regular epsilon for the permittivity constant? I see nothing but the varepsilon symbol except on the Wolfram (http://scienceworld.wolfram.com/physics/PermittivityofFreeSpace.html) science website. --Yath 05:54, 12 Mar 2005 (UTC)

NIST uses a graphic version of that dimpled variant, with alt=" $\varepsilon_0$, at http://physics.nist.gov/cgi-bin/cuu/Value?ep0|search_for=electric+constant

But what I'm wondering is why, if you are so nitpicky about the shape of the epsilon, you aren't also jumping in to change the obsolete "permittivity" to "electric constant"? Gene Nygaard 06:10, 12 Mar 2005 (UTC)

Because I'm not aware of any overriding authority that can be cited to definitively set the symbol and/or name of this value. I'm going by usage, which seems (and I could be wrong) to be varepsilon for the symbol, and "permittivity of free space" for the name.

So I'm waiting to see if Rbj or someone knows of an authority that people should follow, like the BIPM or something. --Yath 16:16, 12 Mar 2005 (UTC)

i'll do a survey of usage from online and printed references. my EE fields text and my undergrad physics texts use the symbol <math> \epsilon_0 \ <math>. i think also NIST. i don't think i ever edited physical constants and they use the same symbol. frankly i don't care but it should be utterly self-consistent and mostly consistent with the usage in the literature. r b-j 22:58, 12 Mar 2005 (UTC)

NIST is kinda funny. if you go to [1] (http://physics.nist.gov/cgi-bin/cuu/Value?ep0) , you get it Yath's version, if you hit the symbol to get its definition in terms of more fundamental constants, you get [2] (http://physics.nist.gov/cgi-bin/cuu/Value?eqep0) , which is what i have been saying. it would be nice if, even they could be self-consistent. their PDF of physical constants has it like <math> \epsilon_0 \ <math>. r b-j 23:08, 12 Mar 2005 (UTC)