The Biot-Savart law gives the magnetic field $d\vec{B}$ due to a small current element $Id\vec{l}$: $d\vec{B} = \frac{\mu_0}{4\pi}\frac{Id\vec{l} \times \hat{r}}{r^2}$. Key features: (1) $dB \propto I$ and $\propto 1/r^2$ (inverse square, like Coulomb's law). (2) Direction is perpendicular to both $d\vec{l}$ and $\hat{r}$ (cross product). (3) The field is zero along the axis of the current element ($\theta = 0$ or $\pi$). (4) Maximum field is in the plane perpendicular to the element ($\theta = \pi/2$). The total field is obtained by integrating over the entire current-carrying conductor.