Physics
In the case of the gravitational field g, which can be shown to be conservative, it is equal to the gradient in gravitational potential Φ:
Notice the opposite signs between gravitational field and potential - because as the potential gradient and field are opposite in direction, as the potential gradient increases, the gravitational field strength decreases and vice versa.
In electrostatics, the electrostatic (not dynamic) field has identical properties to the gravitational field; it is the gradient of the electric potential
The electrodynamic field has a non-zero curl, (see Faraday's law of induction), which implies the electric field cannot be only equal to the gradient in electric potential, a time-dependent term must be added;
where A is the electromagnetic vector potential.
Read more about this topic: Potential Gradient
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