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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form as follows:

The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Electromagnetism, electric flux is Flux of the Electric field. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field Electrostatic induction is a redistribution of Electrical charge in an object caused by the influence of nearby charges In Physics, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges. Charles Augustin de Cock (June 14 1736 Angoulême France – August 23 1806 Penis France was a French Physicist. In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or In Physics, a force is whatever can cause an object with Mass to Accelerate. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. This article is about proportionality the mathematical relation

1 Scalar form
- 1.1 Electric field
2 Vector form
3 Electrostatic approximation
4 Table of derived quantities
5 See also
6 Footnotes
7 References
8 External links

Scalar form

Diagram describing the basic mechanism of Coulomb's law; like charges repel each other and opposite charges attract each other.

Coulomb's torsion balance

If one does not require the specific direction of the force then the simplified, scalar, version of Coulomb's law will suffice. A torsion spring is a spring that works by torsion or twisting that is a flexible elastic object that stores Mechanical energy when it is twisted In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or The magnitude of the force on a charge, $\scriptstyle{q_1}$ , due to the presence of a second charge, $\scriptstyle{q_2}$ , is given by the magnitude of

$F = {1 \over 4\pi\varepsilon_0}\frac{q_1q_2}{r^2}$ ,

where $\scriptstyle{r}$ is the separation of the charges and $\scriptstyle{\varepsilon_0}$ is the electric constant. Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical A positive force implies a repulsive interaction, while a negative force implies an attractive interaction. ^[1]

The prefactor, termed the Coulomb's constant ( $\scriptstyle{k_e}$ ), is:

$\begin{align} k_e &= \frac{1}{4\pi\varepsilon_0} = \frac{\mu_0\ {c_0}^2}{4 \pi} = 10^{-7}\ {c_0}^2 \\ &= 8.987\ 551\ 787\ \times 10^9 \\ \end{align}$

$\approx 9 \times 10^9$ N m²C⁻² (also m F⁻¹). The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International This is about the capacitance unit of measure For the charge unit see Faraday (unit. ^[2]

In SI units the speed of light in vacuum c₀ is defined^[3] as the numerical value c₀ = 299 792 458 m s⁻¹ (See c₀) and the magnetic constant μ₀ is defined as 4π x 10⁻⁷ H · m⁻¹ (See μ₀), leading to the definition for the electric constant of ε₀ = 1/(μ₀c₀²) ≈ 8. The vacuum permeability, referred to by international standards organizations as the magnetic constant, and denoted by the symbol μ 0 (also Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical 854 187 817 x 10⁻¹² F m⁻¹ (See NIST ε₀). In cgs units, the unit charge, esu of charge or statcoulomb, is defined so that this Coulomb force constant is 1. The centimetre-gram-second system ( CGS) is a system of physical units. The statcoulomb ( statC) or franklin ( Fr) or electrostatic unit of charge ( esu) is the physical unit for Electrical

This formula says that the magnitude of the force is directly proportional to the magnitude of the charges of each object and inversely proportional to the square of the distance between them. This article is about proportionality the mathematical relation In Physics, an inverse-square law is any Physical law stating that some physical Quantity or strength is inversely proportional The exponent in Coulomb's Law has been found to differ from −2 by less than one in a billion. ^[4]

When measured in units that people commonly use (such as SI—see International System of Units), the electrostatic force constant, $\scriptstyle{k_e}$ , is numerically much much larger than the universal gravitational constant $\scriptstyle{G}$ . The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass ^[5] This means that for objects with charge that is of the order of a unit charge (C) and mass of the order of a unit mass (kg), the electrostatic forces will be so much larger than the gravitational forces that the latter force can be ignored. This is not the case when Planck units are used and both charge and mass are of the order of the unit charge and unit mass. Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899 However, charged elementary particles have mass that is far less than the Planck mass while their charge is about the Planck charge so that, again, gravitational forces can be ignored. In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made For example, the electrostatic force between an electron and a proton, which constitute a hydrogen atom, is almost 40 orders of magnitude greater than the gravitational force between them. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny An order of magnitude is the class of scale or magnitude of any amount where each class contains values of a fixed ratio to the class preceding it ^[6]

Coulomb's law can also be interpreted in terms of atomic units with the force expressed in Hartrees per Bohr radius, the charge in terms of the elementary charge, and the distances in terms of the Bohr radius. Atomic units ( au) form a System of units convenient for Atomic physics, Electromagnetism, and Quantum electrodynamics, especially A hartree (symbol E h is the atomic unit of Energy and is named after Physicist Douglas Hartree. In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried

Electric field

Main article: Electric field

It follows from the Lorentz Force Law that the magnitude of the electric field $\scriptstyle{\mathbf{E}}$ created by a single point charge $\scriptstyle{q}$ is given by

$E = {1 \over 4\pi\varepsilon_0}\frac{q}{r^2}$

For a positive charge $\scriptstyle{q}$ , the direction of $\scriptstyle{\mathbf{E}}$ points along lines directed radially away from the location of the point charge, while the direction is the opposite for a negative charge. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The units of electric field are volts per meter or newtons per coulomb. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force.

Vector form

In order to obtain both the magnitude and direction of the force on a charge, $\scriptstyle{q_1}$ at position $\scriptstyle{\mathbf{r}_1}$ , experiencing a field due to the presence of another charge, $\scriptstyle{q_2}$ at position $\scriptstyle{\mathbf{r}_2}$ , the full vector form of Coulomb's law is required.

$\mathbf{F} = {1 \over 4\pi\varepsilon_0}{q_1q_2(\mathbf{r}_1 - \mathbf{r}_2) \over |\mathbf{r}_1 - \mathbf{r}_2|^3} = {1 \over 4\pi\varepsilon_0}{q_1q_2 \over r^2}\mathbf{\hat{r}}_{21}$ ,

where $\scriptstyle{r}$ is the separation of the two charges. Note that this is simply the scalar definition of Coulomb's law with the direction given by the unit vector, $\scriptstyle{\mathbf{\hat{r}}_{21}}$ , parallel with the line from charge $\scriptstyle{q_2}$ to charge $\scriptstyle{q_1}$ . In Mathematics, a unit vector in a Normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length ^[6]

If both charges have the same sign (like charges) then the product $\scriptstyle{q_1q_2}$ is positive and the direction of the force on $\scriptstyle{q_1}$ is given by $\scriptstyle{\mathbf{\hat{r}}_{21}}$ ; the charges repel each other. The plus and minus signs ( + and &minus) are Mathematical symbols used to represent the notions of positive and negative as well as the operations In Mathematics, scalar multiplication is one of the basic operations defining a Vector space in Linear algebra (or more generally a module in If the charges have opposite signs then the product $\scriptstyle{q_1q_2}$ is negative and the direction of the force on $\scriptstyle{q_1}$ is given by $-\scriptstyle{\mathbf{\hat{r}}_{21}}$ ; the charges attract each other.

System of discrete charges

The principle of linear superposition may be used to calculate the force on a small test charge, $\scriptstyle{q}$ , due to a system of $\scriptstyle{N}$ discrete charges:

$\mathbf{F}(\mathbf{r}) = {q \over 4\pi\varepsilon_0}\sum_{i=1}^N {q_i(\mathbf{r} - \mathbf{r}_i) \over |\mathbf{r} - \mathbf{r}_i|^3} = {q \over 4\pi\varepsilon_0}\sum_{i=1}^N {q_i \over R_{i}^2}\mathbf{\hat{R}}_{i}$ ,

where $\scriptstyle{q_i}$ and $\scriptstyle{\mathbf{r}_i}$ are the magnitude and position respectively of the $\scriptstyle{i^{th}}$ charge, $\scriptstyle{\mathbf{\hat{R}}_{i}}$ is a unit vector in the direction of $\scriptstyle{\mathbf{R}_{i} = \mathbf{r} - \mathbf{r}_i}$ (a vector pointing from charge $\scriptstyle{q_i}$ to charge $\scriptstyle{q}$ ), and $\scriptstyle{R_{i}}$ is the magnitude of $\scriptstyle{\mathbf{R}_{i}}$ (the separation between charges $\scriptstyle{q_i}$ and $\scriptstyle{q}$ ). In Physics and Systems theory, the superposition principle, also known as superposition property, states that for all Linear systems ^[6]

Continuous charge distribution

For a charge distribution an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge $\scriptstyle{dq}$ . The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Infinitesimals (from a 17th century Modern Latin coinage infinitesimus, originally referring to the " Infinite[[ th]]" member of a series have

For a linear charge distribution (a good approximation for charge in a wire) where $\scriptstyle{\lambda(\mathbf{r^\prime})}$ gives the charge per unit length at position $\scriptstyle{\mathbf{r^\prime}}$ , and $\scriptstyle{dl^\prime}$ is an infinitesimal element of length,

$dq = \lambda(\mathbf{r^\prime})dl^\prime$ . ^[7]

For a surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor) where $\scriptstyle{\sigma(\mathbf{r^\prime})}$ gives the charge per unit area at position $\scriptstyle{\mathbf{r^\prime}}$ , and $\scriptstyle{dA^\prime}$ is an infinitesimal element of area,

$dq = \sigma(\mathbf{r^\prime})dA^\prime$ . A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors

For a volume charge distribution (such as charge within a bulk metal) where $\scriptstyle{\rho(\mathbf{r^\prime})}$ gives the charge per unit volume at position $\scriptstyle{\mathbf{r^\prime}}$ , and $\scriptstyle{dV^\prime}$ is an infinitesimal element of volume,

$dq = \rho(\mathbf{r^\prime})dV^\prime$ . ^[6]

The force on a small test charge $\scriptstyle{q^\prime}$ at position $\scriptstyle{\mathbf{r}}$ is given by

$\mathbf{F} = q^\prime\int dq {\mathbf{r} - \mathbf{r^\prime} \over |\mathbf{r} - \mathbf{r^\prime}|^3}$ .

Graphical representation

Below is a graphical representation of Coulomb's law, when $\scriptstyle{q_1q_2 > 0}$ . The vector $\scriptstyle{\mathbf{F}_1}$ is the force experienced by $\scriptstyle{q_1}$ . The vector $\scriptstyle{\mathbf{F}_2}$ is the force experienced by $\scriptstyle{q_2}$ . Their magnitudes will always be equal. The vector $\scriptstyle{\mathbf{r}_{21}}$ is the displacement vector between two charges ( $\scriptstyle{q_1}$ and $\scriptstyle{q_2}$ ).

A graphical representation of Coulomb's law.

Electrostatic approximation

In either formulation, Coulomb's law is fully accurate only when the objects are stationary, and remains approximately correct only for slow movement. These conditions are collectively known as the electrostatic approximation. Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical When movement takes place, magnetic fields are produced which alter the force on the two objects. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges The magnetic interaction between moving charges may be thought of as a manifestation of the force from the electrostatic field but with Einstein's theory of relativity taken into consideration. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism.

Table of derived quantities

Particle property

Relationship

Field property

Vector quantity

Force (on 1 by 2)

$\mathbf{F}_{12}= {1 \over 4\pi\varepsilon_0}{q_1 q_2 \over r^2}\mathbf{\hat{r}}_{21} \$

$\mathbf{F}_{12}= q_1 \mathbf{E}_{12}$

Electric field (at 1 by 2)

$\mathbf{E}_{12}= {1 \over 4\pi\varepsilon_0}{q_2 \over r^2}\mathbf{\hat{r}}_{21} \$

Relationship

$\mathbf{F}_{12}=-\mathbf{\nabla}U_{12}$

$\mathbf{E}_{12}=-\mathbf{\nabla}V_{12}$

Scalar quantity

Potential energy (at 1 by 2)

$U_{12}={1 \over 4\pi\varepsilon_0}{q_1 q_2 \over r} \$

$U_{12}=q_1 V_{12} \$

Potential (at 1 by 2)

$V_{12}={1 \over 4\pi\varepsilon_0}{q_2 \over r}$

Footnotes

^ Coulomb's law, Hyperphysics
^ Coulomb's constant, Hyperphysics
^ Current practice is to use c₀ to denote the speed of light in vacuum according to ISO 31. The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in Electrostatics. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Charles Augustin de Cock (June 14 1736 Angoulême France – August 23 1806 Penis France was a French Physicist. In Physics, the electromagnetic force is the force that the Electromagnetic field exerts on electrically charged particles International Standard ISO 31 ( Quantities and units International Organization for Standardization, 1992 is the most widely respected style guide for the In the original Recommendation of 1983, the symbol c was used for this purpose. See NIST Special Publication 330, Appendix 2, p. 45
^ Williams, Faller, Hill (1971), “New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass”, Physical Review Letters 26: 721-724, <http://prola.aps.org/abstract/PRL/v26/i12/p721_1>
^ This large ratio has led to the Dirac large numbers hypothesis. Physical Review Letters is one of the most prestigious journals in Physics. The Dirac large numbers hypothesis (LNH refers to an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales
^ ^a ^b ^c ^d Coulomb's law, University of Texas
^ Charged rods, PhysicsLab. org

References

Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed. ). Prentice Hall. ISBN 0-13-805326-X.
Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed. ). W. H. Freeman. ISBN 0-7167-0810-8.

External links

Coulomb's Law on Project PHYSNET.
Electricity and the Atom— - a chapter from an online textbook
A maze game for teaching Coulomb's Law—a game created by the Molecular Workbench software

Dictionary

Coulomb's law

-proper noun

(physics) the fundamental law of electrostatics - the force between two point charges is proportional to the product of their charges, and inversely proportional to the square of the distance between them

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