Vector Potential

Sometimes, vector fields can be represented as the curl of other vector fields known as vector potentials.

Definition §

Vector Potential

Let $\vec{F}$ be a $C^1$ incompressible vector field (that is, $\nabla \cdot \vec{F}=0$). Then, there exists another vector field $\vec{V}$ such that:

$$\vec{F}=\nabla \times \vec{V}$$

That is, $\vec{F}$ can be represented as the curl of $\vec{V}$

• $\vec{V}$ is called the vector potential of $\vec{F}$
• $\vec{V}$ is not unique!

#todo EXAMPLE!!!!