Coulomb Force

Information about Coulomb Force

Electrostatics

Electromagnetism
Electricity Magnetism
Electric charge
Coulomb's law
Electric field
Gauss's law
Electric potential
Electric dipole moment
Magnetostatics
Ampre's circuital law
Magnetic field
Magnetic flux
Biot-Savart law
Magnetic dipole moment
Electrodynamics
Electrical 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
Electrical conduction
Electrical resistance
Capacitance
Inductance
Impedance
Resonant cavities
Waveguides
Tensors in Relativity
Electromagnetic tensor
Electromagnetic stress-energy tensor
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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:

The magnitude of the electrostatic force between two points 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.

Scalar form

If one is interested only in the magnitude of the force, and not in its direction, it may be easiest to consider a simplified, scalar version of the law:

$\text{[math]}$

where:

$\text{[math]}$ is the magnitude of the force exerted,

$\text{[math]}$ is the charge on one body,

$\text{[math]}$ is the charge on the other body,

$\text{[math]}$ is the distance between them,

$\text{[math]}$ 8.988×10⁹ N m² C⁻² (also m F⁻¹) is the electrostatic constant or Coulomb force constant (the number is the square of the speed of light in km/s, divided by 10), and

$\text{[math]}$ 8.854×10⁻¹² C² N⁻¹ m⁻² (also F m⁻¹) is the permittivity of free space, also called electric constant, an important physical constant.

In cgs units, the unit charge, esu of charge or statCoulomb, is defined so that this Coulomb force constant is 1.

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.^[1]

When measured in units that people commonly use (such as MKS - see International System of Units), the Coulomb force constant, $\text{[math]}$ , is numerically much much larger than the universal gravitational constant $\text{[math]}$ . 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 about 40 orders of magnitude greater compared to the gravitational force between them.

The force F acts on the line connecting the two charged objects. Charged objects of the same polarity repel each other along this line and charged objects of opposite polarity attract each other along this line connecting them.

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.

Electric field

It follows from the Lorentz Force Law that the magnitude of the electric field E created by a single point charge q is

For a positive charge q, the direction of E points along lines directed radially away from the location of the point charge, while the direction is the opposite for a negative charge. Units: volts per meter or newtons per coulomb.

Vector form

For the direction and magnitude of the force simultaneously, one will wish to consult the full vector version of Coulomb's Law:

$\text{[math]}$

where

$\text{[math]}$ is the electrostatic force vector, for the force experienced by charge 1 from the action of charge 2.

$\text{[math]}$ is the charge on which the force acts,

$\text{[math]}$ is the acting charge,

$\text{[math]}$ is the vector pointing from charge 2 to charge 1,

$\text{[math]}$ is position vector of $\text{[math]}$ ,

$\text{[math]}$ is the the magnitude of $\text{[math]}$

$\text{[math]}$ is a unit vector pointing in the direction of $\text{[math]}$ , and

$\text{[math]}$ is a constant called the permittivity of free space.

This vector equation indicates that opposite charges attract, and like charges repel. When $\text{[math]}$ is negative, the force is attractive. When positive, the force is repulsive.

Graphical representation

Below is a graphical representation of Coulomb's law, when $\text{[math]}$ . The vector $\text{[math]}$ is the force experienced by $\text{[math]}$ . The vector $\text{[math]}$ is the force experienced by $\text{[math]}$ . Their magnitudes will always be equal. The vector $\text{[math]}$ is the displacement vector between two charges ( $\text{[math]}$ and $\text{[math]}$ ).

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.

Table of derived quantities

Particle property

Relationship

Field property

Vector quantity

Force (on 1 by 2)

$\text{[math]}$

Electric field (at 1 by 2)

$\text{[math]}$

Relationship

$\text{[math]}$

Scalar quantity

Potential energy (at 1 by 2)

Potential (at 1 by 2)

Footnotes

1. ^ 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, <[1]

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.

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.
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Electricity (from New Latin ēlectricus, "amberlike") is a general term for a variety of phenomena resulting from the presence and flow of electric charge. This includes many well-known physical phenomena such as lightning, electromagnetic fields and electric currents,
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magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to
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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 includes phenomena as simple as the attraction of plastic wrap to your hand after you remove it from a
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Flavour in particle physics

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electric field. This electric field exerts a force on other electrically charged objects. The concept of electric field was introduced by Michael Faraday.

The electric field is a vector field with SI units of newtons per coulomb (N C⁻¹
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In physics and mathematical analysis, Gauss's law is the electrostatic application of the generalized Gauss's theorem giving the equivalence relation between any flux, e.g.
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Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. It is a scalar quantity.
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In physics, the electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges.

In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:

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Magnetostatics is the study of static magnetic fields. In electrostatics, the charges are stationary, whereas here, the currents are stationary. As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not
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magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.
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Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field.
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The Biot-Savart Law is an equation in electromagnetism that describes the magnetic field vector B in terms of the magnitude and direction of the source electric current, the distance from the source electric current, and the magnetic permeability weighting factor.
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In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic moment is defined as:

where a
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Classical electromagnetism (or classical electrodynamics) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell.
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.

Definition

The amount of electric current (measured in amperes) through some surface, e.g.
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Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B.
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Electromotive force (emf, ) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors.
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For magnetic induction, see .

Electromagnetic induction is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field.
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Faraday's 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.
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Displacement current is a quantity related to changing electric field. It occurs in dielectric materials and also in free space.

In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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For thermodynamic relations, see .

In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs.
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The electromagnetic field is a physical field produced by electrically charged objects. It affects the behaviour of charged objects in the vicinity of the field.
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Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
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Electrical resistance is a measure of the degree to which an object opposes an electric current through it. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.
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Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The most common form of charge storage device is a two-plate capacitor.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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A resonator is a device or system that exhibits resonance or resonant behavior. Many objects that use resonant effects are referred to simply as resonators. Examples of resonators are discussed in this article.
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theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity.

The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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Coulomb Force

Information about Coulomb Force

Scalar form

Electric field

Vector form

Graphical representation

Electrostatic approximation

Table of derived quantities

See also

Footnotes

References

External links

Definition