Biot-Savart’s law

According to Maxwell’s equations, the only source of a time-independent magnetic field can be due to a current density. The law of Biot-Savart relates the induced magnetic field \(\require{physics} \vb{B}(\vb{r})\) to its inducing current density \(\vb{j}(\vb{r})\): \[\begin{equation} \vb{B}(\vb{r}) = \frac{\mu_0}{4 \pi} \int \dd{\vb{r}'} \frac{ \vb{j}(\vb{r}') \cross (\vb{r} - \vb{r}') }{ \norm{ \vb{r} - \vb{r}' }^3 } \thinspace . \end{equation}\]