| at each point of a given space region, scalar φ the negative of the gradient of which is the vector U of a given irrotational field: U = −grad φ|
NOTE 1 The given vector field U is said to be derived from the scalar potential φ.
NOTE 2 The scalar potential is not unique since any constant scalar can be added to a given scalar potential without changing its gradient.
NOTE 3 An example of scalar potential is the electric potential, the negative of the gradient of which is the electric field strength.
NOTE 4 The term "scalar potential" is only used in place of the term "potential" to distinguish it from the term "vector potential".