Editing Electric field (section)

=== Electrostatics ===
{{main|Coulomb's law}}
In the special case of a [[steady state]] (stationary charges and currents), the Maxwell-Faraday [[inductive effect]] disappears. The resulting two equations (Gauss's law <math>\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}</math> and Faraday's law with no induction term <math>\nabla \times \mathbf{E} = 0</math>), taken together, are equivalent to [[Coulomb's law#Electric field|Coulomb's law]], which states that a particle with electric charge <math>q_1</math> at position <math>\mathbf r_1</math> exerts a force on a particle with charge <math>q_0</math> at position <math>\mathbf r_0</math> of:<ref>Purcell, p7: "... the interaction between electric charges ''at rest'' is described by Coulomb's Law: two stationary electric charges repel or attract each other with a force proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them.</ref>
<math display="block">\mathbf{F}_{01} = \frac{q_1q_0}{4\pi\varepsilon_0} {\hat\mathbf r_{01}\over {|\mathbf r_{01}|}^2} = \frac{q_1q_0}{4\pi\varepsilon_0} {\mathbf r_{01}\over {|\mathbf r_{01}|}^3}</math>
where
* <math> \mathbf{F}_{01} </math> is the force on charged particle <math> q_0 </math> caused by charged particle <math> q_1 </math>.
* {{math|''ε''{{sub|0}}}} is the [[permittivity of free space]].
* <math> \hat \mathbf{r}_{01} </math> is a [[unit vector]] directed from <math> \mathbf r_1 </math> to <math> \mathbf r_0 </math>.
* <math> \mathbf{r}_{01} </math> is the [[displacement vector]] from <math> \mathbf r_1 </math> to <math> \mathbf r_0 </math>.

Note that <math>\varepsilon_0</math> must be replaced with <math>\varepsilon</math>, [[permittivity]], when charges are in non-empty media.
When the charges <math>q_0</math> and <math>q_1</math> have the same sign this force is positive, directed away from the other charge, indicating the particles repel each other. When the charges have unlike signs the force is negative, indicating the particles attract.
To make it easy to calculate the [[Coulomb force]] on any charge at position <math>\mathbf r_0</math> this expression can be divided by <math>q_0</math> leaving an expression that only depends on the other charge (the ''source'' charge)<ref name="Purcell">{{cite book | last1 = Purcell | first1 = Edward | title = Electricity and Magnetism | edition = 2nd | publisher = Cambridge University Press | date = 2011 | pages = 8–9 | url = https://books.google.com/books?id=Z3bkNh6h4WEC&pg=PA8 | isbn = 978-1139503556 }}</ref><ref name="Serway">{{cite book | last1 = Serway | first1 = Raymond A. | last2 = Vuille | first2 = Chris | title = College Physics | edition = 10th | publisher = Cengage Learning | date = 2014 | pages = 532–533 | url = https://books.google.com/books?id=xETAAgAAQBAJ&q=work+energy+capacitor&pg=PA522 | isbn = 978-1305142824 }}</ref>
<math display="block">\mathbf{E}_{1} (\mathbf r_0) = \frac{ \mathbf{F}_{01} } {q_0} = \frac{q_1}{4\pi\varepsilon_0} {\hat\mathbf r_{01}\over {|\mathbf r_{01}|}^2} = \frac{q_1}{4\pi\varepsilon_0} {\mathbf r_{01}\over {|\mathbf r_{01}|}^3}</math>
where: 
* <math>\mathbf{E}_{1} (\mathbf r_0) </math> is the component of the electric field at <math> q_0 </math> due to <math> q_1 </math>.

This is the ''electric field'' at point <math>\mathbf r_0</math> due to the point charge <math>q_1</math>; it is a [[vector-valued function]] equal to the Coulomb force per unit charge that a positive point charge would experience at the position <math>\mathbf r_0</math>.
Since this formula gives the electric field magnitude and direction at any point <math>\mathbf r_0</math> in space (except at the location of the charge itself, <math>\mathbf r_1</math>, where it becomes infinite) it defines a [[vector field]].
From the above formula it can be seen that the electric field due to a point charge is everywhere directed away from the charge if it is positive, and toward the charge if it is negative, and its magnitude decreases with the [[inverse square law|inverse square]] of the distance from the charge.

The Coulomb force on a charge of magnitude <math>q</math> at any point in space is equal to the product of the charge and the electric field at that point
<math display="block">\mathbf{F} = q\mathbf{E} .</math>
The [[Systeme International|SI]] unit of the electric field is the [[newton (unit)|newton]] per [[coulomb]] (N/C), or [[volt]] per [[meter]] (V/m); in terms of the [[SI base unit]]s it is kg⋅m⋅s<sup>−3</sup>⋅A<sup>−1</sup>.