NationMaster - Encyclopedia: Coulomb's law

Electrodynamics
Electric current
Lorentz force law
Electromotive force
(EM) Electromagnetic induction
Faraday-Lenz law
Displacement current
Maxwell's equations
(EMF) Electromagnetic field
(EM) Electromagnetic radiation

Electrical Network
Conduction
Resistance
Capacitance
Inductance
Impedance
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Waveguides

Tensors in Relativity
Electromagnetic tensor
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Coulomb's torsion balance

Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form as follows: Image File history File links Solenoid. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... For other senses of this word, see magnetism (disambiguation). ... Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. ... This box: Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... 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. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... This article does not cite any references or sources. ... This article is about the electromagnetic phenomenon. ... Magnetostatics is the study of static magnetic fields. ... In physics, AmpÃ¨res Circuital law, discovered by AndrÃ©-Marie AmpÃ¨re, relates the circulating magnetic field in a closed loop to the electric current passing through the loop. ... Magnetic field lines shown by iron filings Magnetostatics Electrodynamics Electrical Network Tensors in Relativity This box: In physics, the magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. ... Magnetic flux, represented by the Greek letter Î¦ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ... A bar magnet. ... Classical electrodynamics (or classical electromagnetism) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. ... Electric current is the flow (movement) of electric charge. ... Lorentz force. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ... For magnetic induction, see Magnetic field. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... Displacement current is a quantity related to changing electric field. ... For thermodynamic relations, see Maxwell relations. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... This article does not cite any references or sources. ... Conduction is the movement of electrically charged particles through a transmission medium (electrical conductor). ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Î¦ through the circuit. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... A resonator is a device or part that vibrates (or oscillates) with waves. ... It has been suggested that this article or section be merged with Waveguide (optics). ... In special relativity, in order to more clearly express the fact that Maxwells equations (in vacuum) take the same form in any inertial coordinate system, the vacuum Maxwells equations are written in terms of four-vectors and tensors in the manifestly covariant form (cgs units): , and where is... To meet Wikipedias quality standards, this article or section may require cleanup. ... In physics, the electromagnetic stress-energy tensor is the portion of the stress-energy tensor due to the electromagnetic field. ... Image File history File links Bcoulomb. ... Image File history File links Bcoulomb. ... A torsion spring is a ribbon, bar, or coil that reacts against twisting motion. ... Portrait of Coulomb Charles Augustin Coulomb (June 14, 1736—August 23, 1806) was a French physicist. ... See scalar for an account of the broader concept also used in mathematics and computer science. ...

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.

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

For other uses, see Force (disambiguation). ... This box: Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This article is about proportionality, the mathematical relation. ...

Scalar form

If one does not require the specific direction of the force then the simplified, scalar, version of Coulomb's law will suffice. 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 See scalar for an account of the broader concept also used in mathematics and computer science. ...

$F = {1 over 4pivarepsilon_0}frac{q_1q_2}{r^2}$ ,

where $scriptstyle{r}$ is the separation of the charges and $scriptstyle{varepsilon_0}$ is a constant termed the permittivity of free space. A positive force implies a repulsive interaction, while a negative force implies an attractive interaction.^[1] This article is in need of attention. ...

The prefactor, termed the electrostatic constant ( $scriptstyle{k_C}$ ), assumes the use of SI units and is included to ensure that a pair of one coulomb charges, separated by one metre, each experience a force of one newton. Vacuum permittivity is the electric constant Îµ0 (also known as the permittivity of free space, or by the term dielectric constant of vacuum), which is a fundamental physical constant. ... The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... The coulomb (symbol: C) is the SI unit of electric charge. ... This article is about the unit of length. ... For other uses, see Newton (disambiguation). ...

$k_C = frac{1}{4pivarepsilon_0} approx 8.988 times 10^9$ N m²C⁻² (also m F⁻¹).^[2]

In cgs units, the unit charge, esu of charge or statcoulomb, is defined so that this Coulomb force constant is 1. For other uses, see Newton (disambiguation). ... This article is about the unit of length. ... The coulomb (symbol: C) is the SI unit of electric charge. ... This article is about the unit of length. ... Examples of various types of capacitors. ... This article or section is in need of attention from an expert on the subject. ... The statcoulomb (statC) or franklin (Fr) or electrostatic unit of charge (esu) is the physical unit for electrical charge used in the centimetre-gram-second (cgs) electrostatic system of units. ...

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. The exponent in Coulomb's Law has been found to differ from -2 by less than one in a billion.^[3] This article is about proportionality, the mathematical relation. ... This diagram shows how the law works. ...

When measured in units that people commonly use (such as MKS - see International System of Units), the Coulomb force constant, $scriptstyle{k_C}$ , is numerically much much larger than the universal gravitational constant $scriptstyle{G}$ . 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. 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. 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.^[4] â€œSIâ€ redirects here. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ... In particle physics, an elementary particle is a particle of which other, larger particles are composed. ... For other uses, see Electron (disambiguation). ... For other uses, see Proton (disambiguation). ... This article is about the chemistry of hydrogen. ... Properties For other meanings of Atom, see Atom (disambiguation). ... 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. ...

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 electromagnetism, atomic physics, and quantum electrodynamics, especially when the focus is on the properties of electrons. ... The Hartree energy (symbol Eh) is a physical constant used as atomic unit of energy, 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 (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ...

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 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. ... In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. ... 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. ...

$E = {1 over 4pivarepsilon_0}frac{q}{r^2}$

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. The units of electric field are volts per meter or newtons per coulomb. Josephson junction array chip developed by NIST as a standard volt. ...

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. Look up vector in Wiktionary, the free dictionary. ...

$mathbf{F} = {1 over 4pivarepsilon_0}{q_1q_2(mathbf{r}_1 - mathbf{r}_2) over |mathbf{r}_1 - mathbf{r}_2|^3} = {1 over 4pivarepsilon_0}{q_1q_2 over r^2}mathbf{hat{r}}_{21}$ ,

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 $scriptstyle{q_1}$ .^[4] In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length, (or magnitude) is 1. ...

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. 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. The plus and minus signs (+ and âˆ’) are used to represent the notions of positive and negative as well as the operations of addition and subtraction. ...

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: The principle of Linear superposition describes the sum of two or more disturbances at a point resulting from the simultaneous presence of these disturbances attempting to occupy the same place. ...

$mathbf{F}(mathbf{r}) = {q over 4pivarepsilon_0}sum_{i=1}^N {q_i(mathbf{r} - mathbf{r}_i) over |mathbf{r} - mathbf{r}_i|^3} = {q over 4pivarepsilon_0}sum_{i=1}^N {q_i over R_{i}^2}mathbf{hat{R}}_{i}$ ,

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 $scriptstyle{q}$ ).^[4]

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 $scriptstyle{dq}$ . This article is about the concept of integrals in calculus. ... Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. ...

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,

$dq = lambda(mathbf{r^prime})dl^prime$ .^[5]

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, See Capacitor (component) for a discussion of specific types. ...

$dq = sigma(mathbf{r^prime})dA^prime$ .

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,

$dq = rho(mathbf{r^prime})dV^prime$ .^[4]

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

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

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.

Image File history File links No higher resolution available. ...

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. When movement takes place, magnetic fields are produced which alter the force on the two objects. 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. Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. ... Magnetic field lines shown by iron filings Magnetostatics Electrodynamics Electrical Network Tensors in Relativity This box: In physics, the magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. ... â€œEinsteinâ€ redirects here. ... Two-dimensional analogy of space-time curvature described in General Relativity. ...

Table of derived quantities

Particle property

Relationship

Field property

Vector quantity

Force (on 1 by 2)

$mathbf{F}_{12}= {1 over 4pivarepsilon_0}{q_1 q_2 over r^2}mathbf{hat{r}}_{21}$

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

Electric field (at 1 by 2)

$mathbf{E}_{12}= {1 over 4pivarepsilon_0}{q_2 over r^2}mathbf{hat{r}}_{21}$

Relationship

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

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

Scalar quantity

Potential energy (at 1 by 2)

$U_{12}={1 over 4pivarepsilon_0}{q_1 q_2 over r}$

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

Potential (at 1 by 2)

$V_{12}={1 over 4pivarepsilon_0}{q_2 over r}$

Footnotes

^ Coulomb's law, Hyperphysics
^ Coulomb's constant, Hyperphysics
^ 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>
^ ^a ^b ^c ^d Coulomb's law, University of Texas
^ Charged rods, PhysicsLab.org

Physical Review Letters is one of the most prestigious journals in physics. ...

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

Electricity and the Atom - a chapter from an online textbook
Coulomb's Law on Project PHYSNET.

Categories: Electrostatics | Introductory physics | Fundamental physics concepts

Results from FactBites:

Talk:Coulomb's law - Wikipedia, the free encyclopedia (1008 words)
	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?
	Coulombs law is usually stated as giving the force on a small test charge.
	In typical applications Coulombs law is a very useful approximation.

Electric forces (714 words)
	Coulomb's law is a vector equation and includes the fact that the force acts along the line joining the charges.
	Coulomb's law describes a force of infinite range which obeys the inverse square law, and is of the same form as the gravity force.
	The constant of proportionality k appearing in Coulomb's law is often called Coulomb's constant.

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