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 $\mathbf{B}(\mathbf{r})$ to its inducing current density $\mathbf{j}(\mathbf{r})$: $$\mathbf{B}(\mathbf{r})=\frac{{\mu }_0}{4\pi }\int \mathrm{d}{\mathbf{r}}^{\prime }\frac{\mathbf{j}({\mathbf{r}}^{\prime })\times (\mathbf{r}-{\mathbf{r}}^{\prime })}{{\Vert \mathbf{r}-{\mathbf{r}}^{\prime }\Vert }^3}.$$