A fundamental and empirical law quantifying the electrostatic force between two charges.

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Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the ...
42
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5answers
3k views

Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?

Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges. Gauss's law implies that a the total flux through a ...
26
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4answers
13k views

Why do same/opposite electric charges repel/attract each other, respectively?

I know plus pushes another plus away, but why, really, do they do that? On the other hand, molecules of the same type are attracted to each other. I find that weird. I do know some stuff about four ...
16
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4answers
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Can two electrons get ever so close as to touch each other?

My friend and I were studying for our EM test when we started to think about what happens to the electric field near an infinite line of charge. $$E = \frac{\lambda}{2\pi\rho\epsilon_{0}}$$ As you ...
15
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4answers
1k views

Why are so many forces explainable using inverse squares when space is three dimensional?

It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three ...
15
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2answers
971 views

Is Newton's universal gravitational constant the inverse of permittivity of mass in vacuum?

Is it possible to consider Newton's universal gravitational constant, $G$, as inverse of vacuum permittivity of mass? $$\epsilon_m=\frac {1}{4\pi G}$$ if so, then vacuum permeability of mass will ...
13
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2answers
435 views

Why is there no permittivity-type constant for gravitation?

When I look at electric or magnetic fields, each of them has a constant that defines how a field affects or is affected by a medium. For example, electric fields in vacuum have a permittivity constant ...
12
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3answers
552 views

Coulomb's Law in the presence of a strong gravitational field

I was under the impression that the $1/r^2$ falloff of various forces were because of the way the area of a expanding sphere scales. But that strict $1/r^2$ falloff would only be globally true in a ...
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Coulomb force in SI and cgs

Coulomb force in SI is $ F = \frac{Q1*Q2}{4\pi\varepsilon R^{2}} $ while in CGS $ F = \frac{Q1*Q2}{R^{2}} $ why is it? I mean doesn't it any make difference in dimension? since $ \varepsilon $ ...
11
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6answers
890 views

What is the range of the validity of Coulomb's law?

What is the smallest and biggest distance in which Coulomb's law is valid? Please provide a reference to a scientific journal or book. Just saying that this law is valid from this range to that range ...
11
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2answers
1k views

Using photons to explain electrostatic force

I am trying to understand the idea of a force carrier with the following example. Let's say there are two charges $A$ and $B$ that are a fixed distance from each other. What is causing the force on ...
10
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4answers
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Are the Maxwell's equations enough to derive the law of Coulomb?

Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb? If I am not mistaken, due to ...
10
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1answer
391 views

How the inverse square law in electrodynamics is related to photon mass?

I have read somewhere that one of the tests of the inverse square law is to assume nonzero mass for photon and then, by finding a maximum limit for it , determine a maximum possible error in ...
9
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7answers
1k views

Why is there a factor of $4\pi$ in certain force equations?

I mean to ask why there is $4\pi$ present in force equations governing electricity? Though all objects in universe are not spherical and circular, the constant of proportionality in both equations ...
9
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3answers
501 views

How would charge be distributed in charged conductors if the Coulomb law was not ${1}/{r^2}$?

Would the excess charge on a conductor move to surface until the electric field inside become zero if the Coulomb law was for example $\frac{1}{r^3}$? If yes, would the distribution $\sigma(x,y)$ be ...
7
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1answer
211 views

Classical vs. quantum energy of the hydrogen atom

If I have an electron and a proton and calculate the classical energy which I get by bringing the electron from infinity to the distance of a Bohr radius to the proton, I get 27.2 eV, but the electron ...
7
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2answers
2k views

Coulomb potential in 2D

I know that the Coulomb potential is logarithmic is two dimensions, and that (see for instance this paper: http://pil.phys.uniroma1.it/~satlongrange/abstracts/samaj.pdf) a length scale naturally ...
7
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1answer
152 views

Does QED provide a closed form for Coulomb logarithms?

The classical models for the integrand as well as the cut-offs in computing the Coulomb logarithm are pretty rough. Does quantum electrodynamics have definite expressions for the quantity ...
6
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2answers
665 views

How does one show using QED that same/opposite electric charges repel/attract each other, respectively?

Why do same charges repel each other and opposite charges attract each other (please explain the phenomenon using real laws of nature (QED) not with the approximation model)?
6
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4answers
429 views

Is Coulomb's law accurate for moving charges?

Can we use Coulomb's law to calculate the force between two charges which are not at rest? If not, what formula should be used to calculate the force? I searched it, but I couldn't find a clear ...
5
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0answers
283 views

Modified Coulomb potential

I'm working through Byron and Fuller's "Mathematics of Classical and Quantum Physics" and came across this problem: If the electric potential of a point charge were $\phi(r) = ...
4
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3answers
443 views

Change in attraction of charged bodies

If I insert a piece of glass between two objects carrying different charges, would they still attract? If they attract, does the piece of glass affect the force of attraction and is there any formula ...
4
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3answers
248 views

Precision of Coulomb's law

Up to which precision has the coulomb law proven to be true? I.e. if you have two electrons in a vacuum chamber, 5 meters appart, have the third order terms been ruled out? Are there any theoretical ...
4
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2answers
163 views

Why can you make two repelling positively charged rods touch? Shouldn't the Coulomb force become infinite?

For a physics lab on the Triboelectric effect, we rubbed two rods with fur which gave both of them a positive charge. We then brought them close together, and they obviously repelled. We then held ...
4
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3answers
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Coulomb's Law: why is $k = \dfrac{1}{4\pi\epsilon_0}$ [duplicate]

This was supposed to be a long question but something went wrong and everything I typed was lost. Here goes. Why is $k = \dfrac{1}{4\pi\epsilon_0}$ in Coulomb's law? Is this an experimental fact? ...
4
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2answers
330 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
4
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1answer
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How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?

On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to ...
4
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1answer
287 views

Coulomb interaction as virtual particles exchange?

I've been reading about virtual particle exchanges in physics books and in Physics SA posts, where a particle interpretation of gravity and Coulomb interaction is established. The Feynman Diagram ...
4
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1answer
1k views

What are the limits of applicability of Coulomb's Law?

Coulomb's law is formally parallel to Newton's Law of Universal Gravitation, which is known to give way to General Relativity for very large masses. Does Coulomb's Law have any similar limits of ...
4
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2answers
136 views

Instantaneous Coulomb interaction in QED

It seems I am stuck with a (at a first sight) trivial problem. It's from the "Quarks and Leptons" (Halzen, Martin) book page $141$, where one considers the following integral: $$\tag{1} T_{fi} = ...
3
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2answers
148 views

Relation between Gauss' law and Coulomb's law

In Coulomb's law if the relation was as if electric field intensity was to vary inversely $1/r$ with distance rather than the inverse $1/r^2$ of square of distance, would the Gauss's law still be ...
3
votes
1answer
143 views

Units for physical constants

Someone told me that units for $G$ and $\epsilon_0$ (gravitational constant and Coulomb's constant) are placed there simply to make equations work dimensionally and that there is no real physical ...
3
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1answer
66 views

Why according to Hund's first rule all electron with same spin should occupy orbitals when partially filling?

I get that because of coulomb repulsion initially all the electrons will not occupy the same site but will single occupy the orbitals.But while doing so how do they know to keep their spins aligned ...
3
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1answer
271 views

Information content of the electrostatic Maxwell equations vs Coulomb's Law vs Poisson's Equation

In electrostatics, we have Maxwell's equations: $\nabla \cdot E = \rho$ $\nabla \times E = 0$ These four equations (the second line standing for three equations) can also be written in terms of the ...
3
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1answer
263 views

Coulomb potential

It is known that the Coulomb potential can be obtained by Fourier transform of the propagator from E&M. Is this because one of Maxwell's equations have the form $\nabla \cdot \mathbf{E}=\rho$?
3
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1answer
103 views

The Physics Behind Chemical Bonding

Ok so here's the problem: say I'm a sodium atom. It is 'charged' at +1e. A partner Chlorine atom is flying about, also 'charged' at -1e. According to chemistry (or rather the measurement of the ...
2
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4answers
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The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$?

My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's ...
2
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2answers
322 views

Newton's Law of Graviation: Why $G$ and not e.g. $\dfrac{1}{4\pi G_0}$?

I've been wondering, in Coulomb's Law, $k_e = \dfrac{1}{4\pi\epsilon_0}$. Therefore, why do we use $G$ in Newton's Law of Gravitation? What if the constant is more like Coulomb's Law, e.g. $G = ...
2
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2answers
4k views

Why exactly does current carrying two current wires attract/repel?

When to parallel wires carrying currents in same direction I1 & I2. http://www.youtube.com/watch?v=43AeuDvWc0k this video demonstrates that effect. My question is, why exactly does this happen? ...
2
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2answers
204 views

My conundrum with Gauss’ law in electrostatics

If I use Gauss’ law to calculate the electric field outside of a charged (conducting or insulating) sphere or a point charge, the fields are the same. However, as a test approaches a point charge, the ...
2
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2answers
1k views

Electric potential due to a point charge in Gaussian/CGS units

I learned electrostatics in SI units. In SI, the electrostatic potential due to a point charge $q$ located at $\textbf{r}$ is given by $\Phi(\textbf{r}) = \frac{q}{4 \pi \epsilon_0 |\textbf{r}|}$. ...
2
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2answers
81 views

Electrostatics - Inserting a brass plate between two charges

The question is: if I were to insert a brass plate between two charges, what will happen to the force between the charges? Would it increase, decrease or stay the same? Does the brass plate increase ...
2
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1answer
47 views

What would happen if charged plates are placed horizontally?

My idea is placing charged conducting plates in such a way that they won't see each others' surfaces unlikely to the typical design of parallel plates. If they are placed like this, would be the force ...
2
votes
1answer
96 views

Find the field of two infinite strips of width $b$ [closed]

Q:The two charged strips in the following picture have width $b$, infinite height,and negligible thickness(in the direction perpendicular to the page).Their densities per unit area are $\sigma$ ...
2
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1answer
80 views

Isn't the Coulomb interaction a photon interaction between two charges?

Isn't the Coulomb interaction a photon interaction between two charges? if yes then what does the following text mean? (Many-particle Physics by Gerald D. Mahan.)
2
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0answers
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Is many-body Hamiltonian valid in strong-correlated system

Condensed-matter textbook often states that there is a many-body Hamiltonian $$ H= \sum_i \frac{ p_i^2}{2m_i} + \sum_{i>j} V_{ij} \tag{1} $$ where $V_{ij} = Z_i Z_j/r_{ij}$. This Hamiltonian ...
2
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1answer
59 views

Why do we take the value of the constant in Coulomb's law as $\frac{1}{4\pi\varepsilon_0}$? [duplicate]

Why do we take the value of the constant in Coulomb's law as $\frac{1}{4\pi\varepsilon_0}$?
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3answers
3k views

Similarity between the Coulomb force and Newton's gravitational force

Coulomb force and gravitational force has the same governing equation. So they should be same in nature. A moving electric charge creates magnetic field, so a moving mass should create some force ...
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3answers
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Force inversely proportional to the squared distance

Newton's law of universal gravitation: "Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to ...
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2answers
263 views

Is it possible to calculate the force exerted by two unequal charge, separately?

According to the Coulomb's law, when two equal like point charges are placed 1m from each other the force between them is 9 * 109. But if two unequal like point charges are placed, the bigger charge ...