Vector Potential
#Physics
Any field with 0 divergence can be written as a curl of another vector. $\displaystyle A$ is also not unique to form $\displaystyle \vec{B}$ since we could always add the gradient of some vector to it, as the curl of the gradient of a vector is 0, and curl is distributive
$\displaystyle \nabla \times \vec{A}=\vec{B}$
- $\displaystyle \vec{A}$ is the vector potential
- $\displaystyle \vec{B}$ is the magnetic field
$\displaystyle \vec{A}=\frac{{\mu}_{0}}{4\pi}\int \frac{\vec{J}}{\mathscr{r}} , \mathrm{d}\tau'$
- $\displaystyle \vec{J}$ is the current density
$\displaystyle \nabla \cdot \vec{A}=0$
- In the case of magnetostatics
$\displaystyle \vec{A}=\frac{\vec{B}\times \vec{r}}{2}$
- For constant $\displaystyle \vec{B}$