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 $\mathbf V$.

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {IV}$: The Operator $\nabla$ and its Uses: $2 a$. The Operation $\nabla S$