NCERT · Class 12 · Physics · Moving Charges and MagnetismState Biot-Savart law in vector form.

The Biot-Savart law in vector form expresses the magnetic field $d\mathbf{B}$ at a point due to a current-element $Id\mathbf{l}$ at a distance $\mathbf{r}$. Mathematically, it is written as $d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I(d\mathbf{l} \times \mathbf{r})}{r^3}$, where $\mu_0$ is the permeability of free space, $I$ is the electric current, $d\mathbf{l}$ is the length element vector, and $\mathbf{r}$ is the position vector directed from the current element to the observation point. This fundamental law helps in calculating magnetic induction.