# Talk:Coulomb's law

WikiProject Physics (Rated B-class, Top-importance)
This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
B  This article has been rated as B-Class on the project's quality scale.
Top  This article has been rated as Top-importance on the project's importance scale.
WikiProject Electronics (Rated B-class, Low-importance)
This article is part of WikiProject Electronics, an attempt to provide a standard approach to writing articles about electronics on Wikipedia. If you would like to participate, you can choose to edit the article attached to this page, or visit the project page, where you can join the project and see a list of open tasks. Leave messages at the project talk page
B  This article has been rated as B-Class on the project's quality scale.
Low  This article has been rated as Low-importance on the project's importance scale.
WikiProject Electrical engineering (Rated B-class, High-importance)
This article is within the scope of WikiProject Electrical engineering, a collaborative effort to improve the coverage of Electrical engineering on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
B  This article has been rated as B-Class on the project's quality scale.
High  This article has been rated as High-importance on the project's importance scale.

## Untitled

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....)

Coulombs law is usually stated as giving the force on a small test charge. This simply means that the field due to the test charge should be weak enough not to significantly change the charge distribution producing the original field. DJIndica 07:10, 2 January 2006 (UTC)

## 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)

## Media other than Vacuum

The article is very misleading and actually false in not stating that the equation given for the force between charges is only true if the medium in which the charges are immersed is vacuum. Since many other media could exist the formula should be generalised by including the relative permittivity of the medium as a factor in the equation. The same objection applies to the equation for field in the vicinity of a point charge. It strikes me that to assume that the medium is always vacuum is a very childish and unrealistic position to adopt —Preceding unsigned comment added by 82.32.49.157 (talk) 17:55, 26 March 2011 (UTC)

I fully endorse this. It seems to me that this article adopts a characteristically narrow school-masterly point of view from which all electrostatic experiments are conducted in vacuum, all capacitors are intially discharged, all forces are parallel to displacements, etc, etc. This unrealistic view of the world is not even a good thing to teach to children, and I feel we are entitled to expect better from Wikipedia. I have edited the text somewhat, but feel that it should actually be revised by the original author if he or she is competent to do it. — Preceding unsigned comment added by 82.32.50.178 (talk) 09:27, 21 February 2013 (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 $k \$ in place of $\frac{1}{4 \pi \epsilon_0} \$, but since it was done, the units on $k \$ should be the reciprocal of $\epsilon_0 \$. in addition, the symbol $k \$ 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)

A note on $k \$-- in many introductory textbooks, this constant is given as the numerical version rather than the $\frac{1}{4 \pi \epsilon_0} \$ version, so giving it as both is not a bad idea. As for the confusion with the Boltzmann constant, many letters and symbols are used to mean more than one thing in physics, and if we refrained from using the same leters or symbols over and over again, we would have run out of letters and symbols by the end of mechanics. (Remember, k also stands for the spring constant) It's just a matter of paying attention to what you are studying and knowing which constant they mean. K of slinky 22:55, 9 Sept 2005 (UTC)

The correct units are N m^2 C^{-2}. Also, since the Coulomb constant is defined in terms of the speed of light and the permeability of free space (both of which are known exactly) it's possible to compute the exact value of the Coulomb constant. I've put the exact value (c^2/10^7) in the article. SimpsonDG (talk) 04:36, 31 January 2011 (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 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%7Csearch_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 $\epsilon_0 \$. 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] , you get it Yath's version, if you hit the symbol to get its definition in terms of more fundamental constants, you get [2] , 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 $\epsilon_0 \$. r b-j 23:08, 12 Mar 2005 (UTC)

In Talk:Speaker_wire someone mentioned Coulomb's law in reference to wire length. Does this law apply here, or is it out of context? Lowmagnet 21:52, 25 March 2006 (UTC)

## Point Source used in definition is not defined anywhere

Coulomb's "law" used pith balls and assumed the charge on them could be represented as a point source. There is no definition of point source within Wiki. If I were to add a definition, then it would be that of a mathematical point and I would remove the word source. Bvcrist 20:26, 24 August 2006 (UTC)

point soure or piont charge is that which is apply force` and test charge or force is that which test charge

## k vs. 1/4*pi*Enaught

I've read that the reason k is replaced with 1/4*pi*Enaught is to simplify other formulas and for historical reasons. Can anyone elaborate on this point in the article? I'm interested as to why this is true.

The inclusion of 4pi as a separate factor rather than conflating it with the SI value of epsilon-nought is a characteristic which distinguished the rationalised MKS system from the original MKS system. It is in fact the eponymous rationalisation. The rationalised MKS later evolved into the SI. The reason for separating out the factor 4pi was so that a factor of 4pi or pi would be present in applications which have spherical or circuilar symmetry (as in the present topic of discussion, the force between isolated charges being independent of the direction of r) and absent from those without such symmetries. For example the formula for the capacitance of a coaxial capacitor includes a factor of pi, whereas that for a parallel plate capacitor does not. A factor of pi appears in places where it seems appropriate, and is absent when intuition suggests it is inappropriate. —Preceding unsigned comment added by 82.32.49.157 (talk) 18:10, 26 March 2011 (UTC)

## Trying to figure out electrostatic force without a recursive definition....

I was reading the overview for Coulomb's law, and the first sentance describes how it indicates 'electrostatic force', which is an article that redirects itself to Coulomb's law. Is it just me or is that a little recursive? Or am I way over my head and it is like when the dictionary says that 'redness' is something which exhibits the characteristic of red, for example? Rhetth 16:28, 28 December 2006 (UTC)

## Analogous to huh?

This may be nitpicking, but in the third paragraph, I don't see how Coulomb's law is 'analogous' to Newton's third law. Perhaps in the sense that the force on charge A by charge B is equal and opposite to the force on charge B by charge A. But this is not analogous to Newton's third, it's due to Newton's third. I'd say the analogy would be between Coulomb's law and Newton's law of gravitation. --Chetvorno 23:20, 17 July 2007 (UTC)

## newton

for my point of view it is absolutely not necessary to state anything about "newton" here, esp. not in the introduction. the said about "photons" is also useless. all this following:

" This is analogous to Newton's third law of motion in mechanics. The formula of Coulomb's law is of the same form as Newton's gravitational law: The electrical force of one body exerted on the second body is equal to the force exerted by the second body on the first. Coulomb's law is the mathematical consequence of law of conservation of linear momentum in exchange by virtual photons in 3-dimensional space (see quantum electrodynamics). "

can be deleted without loosing any information. --Pediadeep 13:07, 29 August 2007 (UTC)

## Extra info in "Electrostatic Approximation"

The statement about the accuracy being accurate to within one part in a billion is nice, but it really doesn't go here, and I'm not sure where else it would fit. It's also not sourced. I favor deleting it. Any other opinions? Peppergrower 06:47, 17 October 2007 (UTC)

I am pretty certain that it is essentially correct, and this test of the exponent in the equation should be somewhere in the article. /Pieter Kuiper 07:49, 17 October 2007 (UTC)
Here is the reference: William, Faller, Hill (1971) /Pieter Kuiper 08:05, 17 October 2007 (UTC)

## superconduction re BCS theory

There's nothing here about the exceptions that allow superconductivity. 24.68.233.40 (talk) 01:06, 4 May 2008 (UTC)

I don't know much about BCS theory, but I don't think it has exceptions to Coulomb's law. I believe it adds additional forces between electrons, but leaves the standard electrical repulsion. Foobaz·o< 04:07, 4 May 2008 (UTC)

## error?

I believe there is an error in the integral under "continuous charge distribution". The integral should be multiplied by$k_e$. I'm not 100% sure if i'm right, so I'm going to leave it to someone else to fix it.Sghatch (talk) 16:24, 17 June 2009 (UTC)

## Coulomb's Law and Newton's Law

Does anyone else notice a rather large similarity between $F_e = \frac{kq_1q_2}{r^2}$ and $F_g = \frac{Gm_1m_2}{r^2}$?

Both are to the inverse of the square of the radius (by virtue of three-dimensional space), both are the products of a constant (I'll get to that in a moment) and the values of the two "attributes", and the constant is reflective of the strengths of the forces? And that the sign of the attributes (mass or charge) affects the directionality of the force? Is this not rather good evidence for unification? -RadicalOneContact MeChase My Tail 5:24, 28 January 2010 (UTC)

Technically, to be consistent, there should be a minus sign on the right-hand side of the second equation (Newton's law of gravity), so that in both equations a negative force indicates attraction. The difference in signs of the two equations reflects the fact that two positive masses attract, while two positive charges repel. SimpsonDG (talk) 04:26, 31 January 2011 (UTC)

## Coulomb's predecessors

A number of reliable sources claim that ca. 1760, Daniel Bernoulli discovered Coulomb's law. Many other reliable sources claim that in 1769, Dr. John Robison of Edinburgh, Scotland also discovered Coulomb's law. However, no source provides a citation for these claims. But I'll keep looking.Cwkmail (talk) 11:45, 29 August 2011 (UTC)

## Atomic forces

In the beginning it says: "Coulomb's law states that: "The magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them.""

Then on the section on atomic forces it says: "Coulomb's law holds even within the atoms, correctly describing the force between the positively charged nucleus and each of the negatively charged electrons."

Is it really appropriate to treat the nucleus and the electrons as point charges ? Are there more accurate ways to calculate the electromagnetic force between quarks and electrons ? A link would be useful here.Forcefield2 (talk) 17:41, 3 October 2011 (UTC)

by SineBot-->

## Copyedit of The Law section

I tried to make the first three paragraphs consistent in the following regards:

• math equations are now Tex for the main, article-subject, stand-out ones, and HTML for the inline ones.
• the caption of the diagram needed explaining because the symbols are inconsistent and possibly even |confusing|
• math symbols F, E, r, k, c, q, μ and ε look like the Tex ones (almost)

I think it's MOS compliant.

I also

• moved the descriptive paragraph stating the law to the top.
• removed the wording that almost said 'size of a point'. 'Point charges' is easily intuited.
• moved some sentences around and changed a few words and phrases

Hope that helps. Happy editing! — CpiralCpiral 00:18, 15 August 2012 (UTC)

I reverted some of the many changes IngenieroLoco made. I liked some of them, but either misunderstand or did not like others of them. They are all in the history logs. Let's discuss, please. Let's all use edit summaries. Let's return some of the changes afterwords, after explanations and reasonings beside, as they just now seemed to me to all be, "because". — CpiralCpiral 01:30, 30 August 2012 (UTC)

The changes I made are the following:

• Italics and different paragraph for the law in words.
• Deleted the explanation in brackets in " Coulomb's constant (a proportionality factor sometimes called the electric force constant.) " and added a link to the article of Coulomb's constant.
• I separated the explanation for the Coulomb's constant in a different section.
• I deleted this paragraph totally:
In the more useful vector-form statement, the force in the equation is a vector force acting on either point charge, so directed as to push it away from the other point charge; the right-hand side of the equation, in this case, must have an additional product term of a unit vector pointing in one of two opposite directions, e.g., from q 1  to q 1  if the force is acting on q 2 ; the charges may have either sign and the sign of their product determines the ultimate direction of that force. Thus, the vector force pushing the charges away from each other (pulling towards each other if negative) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The square of the distance part arises from the fact that the force field due to an isolated point charge is uniform in all directions and gets "diluted" with distance as much as the area of a sphere centered on the point charge expands with its radius.
• Changed the vector form of the law from:
$\boldsymbol{F}={q_1q_2\over4\pi\varepsilon_0}{(\boldsymbol{r_1-r_2})\over|\boldsymbol{r_1-r_2}|^3}={q_1q_2\over4\pi\varepsilon_0}{\boldsymbol{\hat{r}_{21}}\over r^2},$

where $r$ is the separation of the two charges.

to

$\boldsymbol{F}={q_1q_2\over4\pi\varepsilon_0}{(\boldsymbol{r_1-r_2})\over|\boldsymbol{r_1-r_2}|^3}={q_1q_2\over4\pi\varepsilon_0}{\boldsymbol{\hat{r}_{21}}\over r_{21}^2},$

where $\boldsymbol{r_{21}}=\boldsymbol{r_1-r_2}$ and $\varepsilon_0$ is the electric constant.

• Fixed two doubles $\boldsymbol{\hat{r}_{21}}\hat{r}_{21}$.
• Fixed the formula for the system:
$\boldsymbol{F(r)}={q\over4\pi\varepsilon_0}\sum_{i=1}^Nq_i{\boldsymbol{r-r_i}\over|\boldsymbol{r-r_i}|^3}={q\over4\pi\varepsilon_0}\sum_{i=1}^Nq_i{\boldsymbol{\widehat{R_i}}\over|\boldsymbol{R_i}|^3},$
$\boldsymbol{F(r)}={q\over4\pi\varepsilon_0}\sum_{i=1}^Nq_i{\boldsymbol{r-r_i}\over|\boldsymbol{r-r_i}|^3}={q\over4\pi\varepsilon_0}\sum_{i=1}^Nq_i{\boldsymbol{\widehat{R_i}}\over|\boldsymbol{R_i}|^2},$

--IngenieroLoco (talk) 09:27, 30 August 2012 (UTC)

After giving your Law section edits a once over, I think I can see your vision with your "entire section" for Coulomb's constant. If we do that then we might as well put the Electric field section next to it, and place them before the detailed math explanations. But then we needed to have the law in minimal word and math forms in the intro to the Law section. Finally, I made the scalar form an "entire sections" in its own right, just like the vector form has.

Then I revisited the layout of the entire article. Images were floating meaninglessly, unmentioned. The article needs fleshing out with much more text before it can improve further. — CpiralCpiral 21:41, 31 August 2012 (UTC)

The words "tested heavily" currently link to "Precision Tests of QED". None of the tests listed there are tests of Coulomb's Law, although. This link needs to be fixed. — Preceding unsigned comment added by 18.111.69.134 (talk) 22:55, 30 August 2012 (UTC)

## r sub 21?

I understand I'm probably missing something here, but that's just the issue. I'm just a student studying electromagnetism in physics class, but it seems like this requires some explaining. In class, we just simply use Fe=(k)q1q2/r2 for our equations. There is no r21 to speak of. I did a little searching and found that someone commented, saying r21=r2-r1, but that's still very unclear for someone who's just looking at this for studying reasons. Can someone maybe add a clarification on the article? --76.118.133.93 (talk) 20:19, 17 April 2013 (UTC)

Hi! I read this and thought you just require a small clarification. Here it is: As force is a vector, so it requires a direction. But the formula you have given above contains all scalars, so it gives just the magnitude of that force. To get a vector, we multiply the magnitude of the vector with a unit vector specifying its direction. And in this case, to get a force vector, we multiply the force magnitude with a unit vector in the same direction as the force (r21 as shown in the diagram in the article). That’s the reason for using a new unit vector r21 here. I hope its clear now.
— Syɛd Шαмiq Aнмɛd Hαsнмi (тαlк) 21:00, 17 April 2013 (UTC)
The formula you use in class is just the scalar form of Coulomb's law and it's also in the article. --IngenieroLoco (talk) 21:36, 17 April 2013 (UTC)

## Potential versus Electric Field

There is an showing both the potential and electric field however from the Article and the diagram, I'm not clear what the difference is. Please could someone clarify this? --Holyone2 (talk) 11:50, 30 May 2013 (UTC)

## Reader feedback: if the charges are of unequa...

39.54.170.102 posted this comment on 19 October 2012 (view all feedback).

if the charges are of unequal magnitude then the magnitude of the forces applied by one on other would be different,how would be that force calculated?

The forces will be the same and they can be calculated using the same formula, just replace q1 and q2 by the value of the charges in the formula.

$|\boldsymbol{F}|=k_e{|q_1q_2|\over r^2}$

IngenieroLoco (talk) 15:41, 9 July 2013 (UTC)

## Electrostatic approximation/ Atomic forces

The accuracy of Coulomb's law requires static point charges. The atomic forces section indicates that the law correctly predicts the interaction between the nucleons and the orbiting electrons, and, presumably, between the orbiting electrons themselves. Those orbiting electrons not only move much more rapidly than "slowly", but are spinning, and, in some cases, changing to excited states (among other things). This sounds like a contradiction. I'm assuming this means that the law applies, and correctly predicts the interactive electostatic force at any instant in time. If so, shouldn't that be clarified in the atomic forces section? — Preceding unsigned comment added by 70.231.130.70 (talk) 00:31, 29 December 2013 (UTC)