# Electric field

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.[1] [2] Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge, by an infinitesimal test charge at that point.[3][4][5] The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, and by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. The electric field and the magnetic field together form the electromagnetic force, one of the four fundamental forces of nature.

From Coulomb's law a particle with electric charge ${\displaystyle q_{1}}$ at position ${\displaystyle {\boldsymbol {x_{1}}}}$ exerts a force on a particle with charge ${\displaystyle q_{0}}$ at position ${\displaystyle {\boldsymbol {x_{0}}}}$ of

When the charges ${\displaystyle q_{0}}$ and ${\displaystyle q_{1}}$ 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 ${\displaystyle {\boldsymbol {x_{0}}}}$ this expression can be divided by ${\displaystyle q_{0}}$, leaving an expression that only depends on the other charge (the source charge)[4][5]

This is the electric field at point ${\displaystyle {\boldsymbol {x_{0}}}}$ due to the point charge ${\displaystyle q_{1}}$; it is a vector equal to the Coulomb force per unit charge that a positive point charge would experience at the position ${\displaystyle {\boldsymbol {x_{0}}}}$. Since this formula gives the electric field magnitude and direction at any point ${\displaystyle {\boldsymbol {x_{0}}}}$ in space (except at the location of the charge itself, ${\displaystyle {\boldsymbol {x_{1}}}}$, 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 of the distance from the charge.

If there are multiple charges, the resultant Coulomb force on a charge can be found by summing the vectors of the forces due to each charge. This shows the electric field obeys the superposition principle: the total electric field at a point due to a collection of charges is just equal to the vector sum of the electric fields at that point due to the individual charges.[5][6]

This is the definition of the electric field due to the point source charges ${\displaystyle q_{1}\cdots q_{N}}$. It diverges and becomes infinite at the locations of the charges themselves, and so is not defined there.

The Coulomb force on a charge of magnitude ${\displaystyle q}$ at any point in space is equal to the product of the charge and the electric field at that point

The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m); in terms of the SI base units they are kg⋅m⋅s−3⋅A−1

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