Definition:Vector Potential

Definition
Let $R$ be a region of ordinary space.

Let $\mathbf V$ be a vector field over $R$.

Let $\mathbf V$ be both rotational and solenoidal.

Let $\mathbf A$ be a vector field such that $\mathbf V = \curl \mathbf A$.

Then $\mathbf A$ is known as the vector potential of $\mathbf V$.