Question

The Biot Savart's Law in vector form is

Answer 1

The Biot Savart's Law we know is given by:

$\overrightarrow{\delta B}=\frac{{\mu }_0}{4\pi }\frac{Idl\sin \left(\theta \right)}{r^2}\hat{r}$, where $\theta$ is the angle between the line element $\overrightarrow{dl}$ and the radial unit vector $\hat{r}$.

Now we know: $\hat{r}=\frac{\overrightarrow{r}}{r}$, using this and the cross product of two vectors we get; $\overrightarrow{\delta B}=\frac{{\mu }_0}{4\pi }\frac{I(\overrightarrow{dl}\times \overrightarrow{r})}{r^3}$