(i) Write an expression of Biot-Savart law in vector form. (ii) State Ampere's circuital law. Write…

The Biot-Savart law in vector form for a current element $I d\vec{l}$ at position vector $\vec{r}$ is: $d\vec{B} = \frac{\mu_{0}}{4\pi} \frac{I (d\vec{l} \times \vec{r})}{r^{3}}$ or $d\vec{B} = \frac{\mu_{0}}{4\pi} \frac{I (d\vec{l} \times \hat{r})}{r^{2}}$

Ampere's circuital law states that the line integral of magnetic field $\vec{B}$ around any closed path/loop in vacuum is equal to $\mu_{0}$ times the total current $I_{\text{enclosed}}$ threading through the area bounded by the path: $\oint \vec{B} \cdot d\vec{l} = \mu_{0} I_{\text{enclosed}}$