Electrostatic Fields
Electrostatic fields are E-fields which do not change with time, which happens when the charges are stationary.
The electric field at a point E(r) is equal to the negative gradient of the electric potential Φ(r), a scalar field at the same point:
where ∇ is the gradient. This is equivalent to the force definition above, since electric potential Φ is defined by the electric potential energy U per unit (test) positive charge:
and force is the negative of potential energy gradient:
If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may also be defined.
Read more about this topic: Electric Field
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—Henry David Thoreau (1817–1862)