# Electric field

The attractive electric field between two charges of opposite sign.
An electric field is a vector field defined as the force per unit charge due to the Coulomb force.[1] When an electrically charged particle is placed in an electric field, it experiences a force, the size and direction of which depends on the amount of charge on the particle. Mathematically this is F=qE. Electric fields are produced by objects with electric charge or by changing magnetic fields.

## Definition

The electric field at any point in space is the force that a positive, stationary unit test charge would experience at that point. For stationary particles, Coulomb's law can be used. Electric fields around positive charges point outwards.

## Important Concepts

### Superposition

The principle of superposition of electric fields states: the resultant electric field due to two or more sources at any point is the vector sum of the electric fields due to each source at that point in space. Put simply, if one charge produces and electric field E1 and another produces an electric field E2, then the electric field when both charges are present is just E1+E2. This property follows from the linearity of Maxwell's equations. This can be extended to and arbitrary number of particles as using a sum if the particles are discrete or an integral if they are continuous.

### Field Lines

Field lines were developed by Michael Faraday as an intuitive way of understanding electric fields.[2] The lines show the direction in which a small positive charge would accelerate. The spacing between lines shows the magnitude of the electric field; areas where lines that are close together mean the electric field is strong in that region. Field lines start on positive charges and go to negative charges.[note 1] In this way positive charges are often called "sources" and negative charges "sinks".

## Electrostatic fields

When charges move and accelerate, they produce currents which can create magnetic fields and which can in turn create further electric fields. A simpler scenario is if all particles are stationary and so do not produce any magnetic fields. In this case, the resultant electic field is known as an electrostatic field (static as in particles do not move).

The electrostatic field around any object can be found by treating it as an infinite number of point particles. As all particles are stationary, Coulomb's law can then be applied. The resultant electric field is the sum of the field of each particle. This is done using integration. Although this method will work for any charge distribution, even for simple shapes it can be very messy. Therefore, if the problem has a lot of symmetry Gauss's law is used instead. Gauss's law enables the field of symmetric distributions to be found in a few lines compared to several pages via integration.

## Notes

1. Technically, electric field lines can also start and end at infinity