Law 0.0.1  The Biot-Savart law states that the magnetic field $\vec{B}$ produced by a current carrying wire, a surface current density $\vec{K}(\vec{r}')$ or a volume current density $\vec{J}(\vec{r})$ in a vacuum is determined by the following integrals.$\newcommand\abs[1]{\left|#1\right|}$
\[\vec{B} = \frac{\mu_0I}{4\pi}\int_L\frac{d\vec{r}'\times\left(\vec{r}-\vec{r}'\right)}{\abs{\vec{r}-\vec{r}'}^3}\]\[\vec{B} = \frac{\mu_0}{4\pi}\int_S\frac{\vec{K}(\vec{r}')\times(\vec{r}-\vec{r}')}{\abs{\vec{r}-\vec{r}'}^3}d^2\vec{r}'\]\[\vec{B} = \frac{\mu_0}{4\pi}\int_V\frac{\vec{J}(\vec{r}')\times(\vec{r}-\vec{r}')}{\abs{\vec{r}-\vec{r}'}^3}d^3\vec{r}'\]