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Coulomb's law

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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 point charges is
   directly proportional to the magnitudes of each charge and inversely
   proportional to the square of the distance between the charges.

   This is analogous to Newton's third law of motion in mechanics. The
   formula to Coulomb's Law is of the same form as Newton's Gravitational
   Law: The electrical force of one body exerted on the second body is
   equal to the force exerted by the second body on the first.

   Coulomb's law is the mathematical consequence of law of conservation of
   linear momentum in exchange by virtual photons in 3-dimensional space
   (see quantum electrodynamics).

Scalar form

   If you are 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:

          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 \epsilon_0} \approx 8.988×10^9 N m^2 C^-2
          (also m F^-1) is the electrostatic constant or Coulomb force
          constant, and
          \epsilon_0 \approx 8.854×10^−12 C^2 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. 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.

   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 \epsilon_0 } \frac{\left|q\right|}{r^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 version of the Law

          \vec{F}_{12} = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2
          }{|\vec{r}_{21}|^3} \vec{r}_{21} = \frac{1}{4 \pi \epsilon_0 }
          \frac{q_1 q_2}{r^2} \hat{r}_{21}

   where

          \vec{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,
          \vec{r}_{21}=\vec{r_1}-\vec{r_2} is the vector pointing from
          charge 2 to charge 1,
          \vec{r_1} \ is position vector of q_1 \ ,
          \vec{r_2} \ is position vector of q_2 \ ,
          r \ is the the magnitude of \vec{r}_{21}
          \hat{r}_{21} is a unit vector pointing in the direction of
          \vec{r}_{21} , and
          \epsilon_0 \ is a constant called the permittivity of free
          space.

   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 \vec{F_1} is the force experienced by Q_1 \ . The vector
   \vec{F_2} is the force experienced by Q_2 \ . Their magnitudes will
   always equal. The vector \vec{R}_{12} is the displacement vector ( = -
   \vec{r}_{21} above, somebody should fix the picture below! ) between
   two charges ( Q_1 \ and Q_2 \ ).
   A graphical representation of Coulomb's law.
   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. When movement takes place, magnetic fields are produced
   that alter the force on the two objects. The magnetic interaction
   between moving charges can be thought of as a manifestation of the
   force from the electrostatic field but with Einstein's theory of
   relativity taken into consideration.

   The accuracy of the exponent in Coulomb's Law has been found to differ
   from two by less than one in a billion by measuring the electric field
   inside a charged conducting shell.

Table of derived quantities

   Particle property Relationship Field property
   Vector quantity
   Force (on 1 by 2)
   \vec{F}_{12}= {1 \over 4\pi\epsilon_0}{q_1 q_2 \over r^2}\hat{r}_{21} \
   \vec{F}_{12}= q_1 \vec{E}_{12}
   Electric field (at 1 by 2)
   \vec{E}_{12}= {1 \over 4\pi\epsilon_0}{q_2 \over r^2}\hat{r}_{21} \
   Relationship \vec{F}_{12}=-\vec{\nabla}U_{12}
   \vec{E}_{12}=-\vec{\nabla}V_{12}
   Scalar quantity
   Potential energy (at 1 by 2)
   U_{12}={1 \over 4\pi\epsilon_0}{q_1 q_2 \over r} \
   U_{12}=q_1 V_{12} \
   Potential (at 1 by 2)
   V_{12}={1 \over 4\pi\epsilon_0}{q_2 \over r}

   Retrieved from " http://en.wikipedia.org/wiki/Coulomb%27s_law"
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   with only minor checks and changes (see www.wikipedia.org for details
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