X-Nico

89 unusual facts about coulomb


Angular momentum coupling

Or two charged particles, each with a well-defined angular momentum, may interact by Coulomb forces, in which case coupling of the two one-particle angular momenta to a total angular momentum is a useful step in the solution of the two-particle Schrödinger equation.

Bell's spaceship paradox

The thread, on the other hand, being a physical object held together by electrostatic forces, maintains the same rest length.

Binet equation

Matching the orbital h^2/l to physical values like GM or k e q 1 q 2/m reproduces Newton's law of universal gravitation or Coulomb's law, respectively.

Bragg's law

Thus, it has been known for many years that, due to repulsive Coulombic interactions, electrically charged macromolecules in an aqueous environment can exhibit long-range crystal-like correlations with interparticle separation distances often being considerably greater than the individual particle diameter.

Carbon nanotube nanomotor

Coulomb's law states that the electrostatic force between two objects is inversely proportional to the square of their distance.

Centimetre–gram–second system of units

The first is Coulomb's law, F = k {\rm C} \frac{q \cdot q^\prime}{d^2}, which describes the electrostatic force F between electric charges q and q^\prime, separated by distance d.

Charles-Augustin de Coulomb

He discovered an inverse relationship of the force between electric charges and the square of its distance, later named after him as Coulomb's law.

He was best known for developing Coulomb's law, the definition of the electrostatic force of attraction and repulsion.

Classical electromagnetism

In electrostatics, where charges are not moving, around a distribution of point charges, the forces determined from Coulomb's law may be summed.

Classical field theory

Using this and Coulomb's law tells us that the electric field due to a single charged particle as

Coulomb barrier

The Coulomb barrier, named after Coulomb's law, which is named after physicist Charles-Augustin de Coulomb (1736–1806), is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a nuclear reaction.

Debye length

The mobile charges not only establish \Phi(\mathbf{r}) but also move in response to the associated Coulomb force, - q j \, \nabla \Phi(\mathbf{r}).

Density functional theory

The effective potential includes the external potential and the effects of the Coulomb interactions between the electrons, e.g., the exchange and correlation interactions.

Dielectrophoresis

The electric field polarizes the particle, and the poles then experience a force along the field lines, which can be either attractive or repulsive according to the orientation on the dipole.

Divergence theorem

Two examples are Gauss' law (in electrostatics), which follows from the inverse-square Coulomb's law, and Gauss' law for gravity, which follows from the inverse-square Newton's law of universal gravitation.

Effective nuclear charge

In this case, the effective nuclear charge can be calculated from Coulomb's law.

Electric charge

Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them.

Electric potential energy

Using Coulomb's law, it is known that the electrostatic force F and the electric field E created by a discrete point charge Q are radially directed from Q.

The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula.

Electric-field screening

In a fluid composed of electrically charged constituent particles, each pair of particles interact through the Coulomb force,

Electroscope

Electroscopes detect electric charge by the motion of a test object due to the Coulomb electrostatic force.

Entropic force

In the paper, three example systems are shown to exhibit such a force electrostatic system of molten salt, surface tension and rubber elasticity.

Euler's three-body problem

Euler's problem also covers the case when the particle is acted upon by other inverse-square central forces, such as the electrostatic interaction described by Coulomb's law.

Euler's three-body problem is to describe the motion of a particle under the influence of two centers that attract the particle with central forces that decrease with distance as an inverse-square law, such as Newtonian gravity or Coulomb's law.

Excimer

Evidence for the bonded exciplex intermediate has been given in studies of steric and Coulombic effects on the quenching rate constants and from extensive Discrete Fourier Transform computations that show a curve crossing between the ground state and the low-energy bonded exciplex state.

Exciton

An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force.

Faddeev equations

The Coulomb interaction between two protons is a special problem, in that its expansion in separable potentials does not converge, but this is handled by matching the Faddeev solutions to long range coulomb solutions, instead of to plane waves.

Field equation

Incidentally, this similarity arises from the similarity between Newton's law of gravitation and Coulomb's law.

Field line

This means that their density is proportional to 1/r^2, the correct result consistent with Coulomb's law for this case.

First quantization

For example, the three quantum numbers n,l,m associated to an electron in a coulomb potential, like the hydrogen atom, form a complete set (ignoring spin).

Force-directed graph drawing

Typically, spring-like attractive forces based on Hooke's law are used to attract pairs of endpoints of the graph's edges towards each other, while simultaneously repulsive forces like those of electrically charged particles based on Coulomb's law are used to separate all pairs of nodes.

Functional derivative

For the electron-nucleus potential, Thomas and Fermi employed the Coulomb potential energy functional

For the classical part of the electron-electron interaction, Thomas and Fermi employed the Coulomb potential energy functional

Gauss's law

In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.

Gauss's law for gravity

Gauss's law for gravity has the same mathematical relation to Newton's law that Gauss's law for electricity bears to Coulomb's law.

Gaussian surface

This non-trivial result shows that any spherical distribution of charge acts as a point charge when observed from the outside of the charge distribution; this is in fact a verification of Coulomb's law.

Green Wheat

The book was written during the vacation of the writer on her property Roz-Ven in Saint-Coulomb, between Saint-Malo and Cancale.

Hartree–Fock method

The first is a sum of kinetic energy operators for each electron, the internuclear repulsion energy, and a sum of nuclear-electronic Coulombic attraction terms.

Hooke's atom

Hooke's atom, also known as harmonium or hookium, refers to an artificial helium-like atom where the Coulombic electron-nucleus interaction potential is

Hydrogen atom

The solution of the Schrödinger equation (wave equations) for the hydrogen atom uses the fact that the Coulomb potential produced by the nucleus is isotropic (it is radially symmetric in space and only depends on the distance to the nucleus).

Interference lithography

A fundamental concern for using low-energy electrons (<<100 eV) with this technique is their natural tendency to repel one another due to Coulomb forces as well as Fermi-Dirac statistics, though electron anti-bunching has been verified only in a single case.

Inverse-square law

The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as Coulomb's law.

Jefimenko's equations

These equations are the time-dependent generalization of Coulomb's law and the Biot-Savart law to electrodynamics, which were originally true only for electrostatic and magnetostatic fields, and steady currents.

Kelvin water dropper

If there is a steady stream of water through the rings, and if the streams are not perfectly centered in the rings, one can observe the deflection of the streams prior to each spark due to the electrostatic attraction via Coulomb's law of opposite charges.

Knot energy

Coulomb's law states that two electric charges of the same sign will repel each other as the inverse square of the distance.

Laplace–Runge–Lenz vector

The hydrogen atom is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law of electrostatics, another inverse square central force.

Length contraction

Though in relativity, the higher-than-expected ionization ability can be explained by length contraction of the Coulomb field in frames in which the ionizing particles are moving, which increases their electrical field strength normal to the line of motion.

Lepton

It determines the strength of the electric field generated by the particle (see Coulomb's law) and how strongly the particle reacts to an external electric or magnetic field (see Lorentz force).

Liouville dynamical system

In classical mechanics, Euler's three-body problem describes the motion of a particle in a plane under the influence of two fixed centers, each of which attract the particle with an inverse-square force such as Newtonian gravity or Coulomb's law.

Maskless lithography

However, a fundamental consideration here is to what degree electrons from neighboring beams can disturb one another (from Coulomb repulsion).

Method of image charges

This situation is equivalent to the original setup, and so the force on the real charge can now calculated with Coulomb's law between two point charges.

Molecular Hamiltonian

The molecular Hamiltonian is a sum of several terms: its major terms are the kinetic energies of the electrons and the Coulomb (electrostatic) interactions between the two kinds of charged particles.

Molecular mechanics

The basic functional form is the Coulomb potential, which only falls off as r−1.

Mott transition

For an electron to move away from a site requires a certain amount of energy, as the electron is normally pulled back toward the (now positively charged) site by Coulomb forces.

Newton's law of universal gravitation

Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies.

Nitrogen laser

After some time the electric charge in the avalanche becomes so large that following Coulomb's law it generates an electric field as large as the external electric field.

Non-Kekulé molecule

According to Hund's rule, each orbital is filled with one electron with parallel spin, avoiding the Coulomb repulsion by filling one orbital with two electrons.

Nonelectrostatic electric fields

The striking difference between the two kinds of fields is that we cannot associate electric potential with points in such an electric field and that the work done by the electric force in such a field is not zero over a closed loop.

P-process

Such proton captures on stable nuclides (or nearly stable), however, are not very efficient in producing p-nuclei, especially the heavier ones, because the electric charge increases with each added proton, leading to an increased repulsion of the next proton to be added, according to Coulomb's law.

Partial charge

Partial atomic charges are used in molecular mechanics force fields to compute the electrostatic interaction energy using Coulomb's law.

Particle in a spherically symmetric potential

In particular, if the particle in question is an electron and the potential is derived from Coulomb's law, then the problem can be used to describe a hydrogen-like (one-electron) atom (or ion).

Periodic boundary conditions

PBC can be used in conjunction with Ewald summation methods (usually particle mesh Ewald) of accounting for electrostatic forces in the system.

Periodic trends

All periodic trends of the chemicals are based on Coulomb's law F C = \frac{k q 1 q 2}{d^2}.

Plasma modeling

A kinetic description is achieved by solving the Boltzmann equation or, when the correct description of long-range Coulomb interaction is necessary, by the Vlasov equation which contains self-consistent collective electromagnetic field, or by the Fokker-Planck equation, in which approximations have been used to derive manageable collision terms.

Point particle

The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges.

Positronium

We also note that a two-body Dirac equation composed of a Dirac operator for each of the two point particles interacting via the Coulomb interaction can be exactly separated in the (relativistic) center of momentum frame and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.

Precision tests of QED

One type of these tests, for example, work by checking Coulomb's law at high accuracy, as Coulomb's law would be modified if the photon mass were nonzero.

Principle of locality

Coulomb's law of electric forces was initially also formulated as instantaneous action at a distance, but was later superseded by Maxwell's Equations of electromagnetism which obey locality.

Protonium

Unlike the hydrogen atom in which the dominant interactions are due to the Coulomb attraction of the electron and the proton, the constituents of protonium interact predominantly through the strong interaction.

Pseudopotential

The pseudopotential is an attempt to replace the complicated effects of the motion of the core (i.e. non-valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulombic potential term for core electrons normally found in the Schrödinger equation.

QIT

Q = It, the formula describing charge in terms of current and time

Quark–gluon plasma

A plasma is matter in which charges are screened due to the presence of other mobile charges; for example: Coulomb's Law is suppressed by the screening to yield a distance-dependent charge.

Quasiparticle

Motion in a solid is extremely complicated: Each electron and proton gets pushed and pulled (by Coulomb's law) by all the other electrons and protons in the solid (which may themselves be in motion).

Sand filter

In addition, particulate solids can be prevented from being captured by surface charge repulsion if the surface charge of the sand is of the same sign (positive or negative) as that of the particulate solid.

Screening effect

In solids, especially in metals and semiconductors, the electrostatic screening or screening effect reduces the electrostatic field and Coulomb potential of an ion inside the solid.

Semiconductor luminescence equations

This description established the first step toward semiconductor quantum optics because the SLEs simultaneously includes the quantized light–matter interaction and the Coulomb-interaction coupling among electronic excitations within a semiconductor.

Stephan W. Koch

(abbreviated as SLEs); the SLEs describe the quantum physics where quantum fluctuations of light initiate incoherent light emission from spontaneous recombination of Coulomb-coupled electron–hole pairs.

Tandem mass spectrometry

If an electron is added to a multiply charged positive ion, the Coulomb energy is liberated.

Tests of special relativity

Contraction also leads to an increase of the intensity of the Coulomb field perpendicular to the direction of motion, whose effects already have been observed.

Thomas–Fermi screening

With k0=0 (no screening), this becomes the familiar Coulomb's law.

Tight binding

This interaction Hamiltonian includes direct Coulomb interaction energy and exchange interaction energy between electrons.

Torsion spring

Determining the force for different charges and different separations between the balls, he showed that it followed an inverse-square proportionality law, now known as Coulomb's law.

Tritium

However, if the atoms have a high enough temperature and pressure (for example, in the core of the Sun), then their random motions can overcome such electrical repulsion (called the Coulomb force), and they can come close enough for the strong nuclear force to take effect, fusing them into heavier atoms.

Vacuum permittivity

where Q is a quantity that represents the amount of electricity present at each of the two points, and ke is Coulomb's constant.

Vlasov equation

The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range (for example, Coulomb) interaction.

First, Vlasov argues that the standard kinetic approach based on the Boltzmann equation has difficulties when applied to a description of the plasma with long-range Coulomb interaction.

Waggle dance

Both low- and high-frequency components emitted by dancing bees induce passive antennal movements in stationary bees according to Coulomb's law.

Water model

The electrostatic interaction is modeled using Coulomb's law and the dispersion and repulsion forces using the Lennard-Jones potential.

World line

For instance, the traditional electro-static force described by Coulomb's law may be pictured in a simultaneous hyperplane, but relativistic relations of charge and force involve retarded potentials.


Rudolf Podgornik

His field of research is the physics of soft matter, the physics of coulomb fluids and macromolecular interactions, the Lifshitz theory of dispersion interaction, the physics of membranes, polymers and polyelectrolytes and especially the physics of DNA and viruses.