Coulomb Force

Coulomb's law - Wikipedia, the free encyclopedia
... of charge or statcoulomb, is defined so that this Coulomb force constant is 1. ... Coulomb's law can also be interpreted in terms of atomic units with the force ...
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Electric forces
Coulomb's law is a vector equation and includes the fact that the force acts ... Coulomb's law describes a force of infinite range which obeys the inverse square ...
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Coulomb's law: Definition from Answers.com
Coulomb's law ( ) n. The fundamental law of electrostatics stating that the force between two charged particles is directly proportional to the
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Coulomb Force
... the case of the electric "Coulomb" force, the magnitude is proportional to the ... The force of gravity is very similar to the Coulomb force; the charges are now ...
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Coulomb's Law
Coulomb's Law. Inverse Square Law. Newton's Laws and the Electrical Force ... The Coulomb's law equation provides an accurate description of the force between ...
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Coulomb force -- Britannica Online Encyclopedia
Britannica online encyclopedia article on Coulomb force:attraction or repulsion of particles or objects because of their electric charge. One of the basic physical ...
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Coulomb's Law - The law of force
Coulomb's Law - The law of force. Any two charged objects will create a force on each other. ... On the other hand, a coulomb is an incredibly large unit of charge. ...
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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 Proportionality (mathematics) 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 (physics) version of the law:

F = k_C \frac{|q_1| |q_2|}{r^2}

where: F \ is the magnitude of the force exerted, q_1 \ is the charge on one body, q_2 \ is the charge on the other body, r \ is the distance between them, k_C = \frac{1}{4 \pi \varepsilon_0} \approx 8.988×109 Newton metre2 Coulomb−2 (also metre Farad−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 \varepsilon_0 \approx 8.854×10−12 Coulomb2 Newton−1 metre−2 (also Farad metre−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 inverse-square law 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.

When measured in units that people commonly use (such as MKS - see International System of Units), the Coulomb force constant, k, is numerically much much larger than the universal gravitational constant 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 about 40 order 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

E = { 1 \over 4 \pi \varepsilon_0 } \frac{q}{\left|r\right|^2}

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 (spatial) version of Coulomb's Law: \mathbf{F}_{12} = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2 }{|\mathbf{r}_{21}|^3} \mathbf{r}_{21} = \frac{1}{4 \pi \varepsilon_0 } \frac{q_1 q_2}{r^2} \mathbf{\hat{r-->_{21} where \mathbf{F}_{12} is the electrostatic force vector, for the force experienced by charge 1 from the action of charge 2. q_1 \ is the charge on which the force acts, q_2 \ is the acting charge, \mathbf{r}_{21}=\mathbf{r_1}-\mathbf{r_2} is the vector pointing from charge 2 to charge 1, \mathbf{r_1} \ is position vector of q_1 \ , \mathbf{r_2} \ is position vector of q_2 \ , r \ is the the magnitude of \mathbf{r}_{21} \mathbf{\hat{r-->_{21} is a unit vector pointing in the direction of \mathbf{r}_{21} , and \varepsilon_0 \ is a constant called the permittivity#Vacuum_permittivity.

This vector equation indicates that opposite charges attract, and like charges repel. When q_1 q_2 \ is negative, the force is attractive. When positive, the force is repulsive.

Graphical representation Below is a graphical representation of Coulomb's law, when q_1 q_2 > 0 \ . The vector \mathbf{F_1} is the force experienced by q_1 \ . The vector \mathbf{F_2} is the force experienced by q_2 \ . Their magnitudes will always be equal. The vector \mathbf{r}_{21} is the displacement vector between two charges ( q_1 \ and q_2 \ ).

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 electrostatics. 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 Albert Einstein's theory of relativity taken into consideration.

Table of derived quantities {| border="1" style="border-collapse: collapse;" cellpadding="15"| ||Particle property||Relationship||Field property|-|-|Vector quantity||{| border="0"|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}||{| border="0"|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||{| border="0"|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} \ ||{| border="0"|Potential (at 1 by 2)|-|V_{12}={1 \over 4\pi\varepsilon_0}{q_2 \over r} |}|}

See also

Biot-Savart Law
Method of image charges
Electric field
Coulomb, the SI unit of electric charge named after Charles Augustin de Coulomb

Footnotes

References

External links

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