\begin{definition}[Definition:Scalar Potential]
Let $R$ be a region of ordinary space.
Let $\mathbf V$ be a conservative vector field over $R$.
By Vector Field is Expressible as Gradient of Scalar Field iff Conservative, there exists a scalar field $S$ over $R$ such that:
:$\grad S = \mathbf V$
where $\grad$ denotes the gradient operator.
Then $S$ is referred to as the '''scalar potential''' of $\mathbf V$.
\end{definition}