# Definition:Scalar Potential

## Definition

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 $\mathbf V$.