An electric field (sometimes E-field) is the physical field that surrounds each electric charge and exerts force on all other charges in the field, either attracting or repelling them. Electric fields originate from electric charges, or from time-varying magnetic fields. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.
Electric fields are important in many areas of physics, and are exploited practically in electrical technology. In atomic physics and chemistry, for instance, the electric field is used to model the attractive force holding the atomic nucleus and electrons together in atoms. It also models the forces in chemical bonding between atoms that result in molecules.
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The derived SI units for the electric field are volts per meter (V/m), exactly equivalent to newtons per coulomb (N/C).
The E and D fields are related by the permittivity of the material, ε.
For linear, homogeneous, isotropic materials E and D are proportional and constant throughout the region, there is no position dependence: