State and explain the Biot-Savart law for the magnetic field produced by a current element. Give the direction of the magnetic field and define its unit.

(N/A) Biot-Savart Law: The magnetic field $d \vec{B}$ at a position vector $\vec{r}$ relative to a current-carrying element $I d \vec{l}$ is given by:
$d \vec{B} = \frac{\mu_0}{4 \pi} \frac{I (d \vec{l} \times \vec{r})}{r^3} = \frac{\mu_0}{4 \pi} \frac{I d l \sin \theta}{r^2} \hat{r}$
According to the Biot-Savart law,the magnitude of the field $d B$ is:
$(1)$ Directly proportional to the current $I$ through the conductor: $d B \propto I$
$(2)$ Directly proportional to the length $|d \vec{l}|$ of the current element: $d B \propto d l$
$(3)$ Directly proportional to $\sin \theta$,where $\theta$ is the angle between $d \vec{l}$ and $\vec{r}$: $d B \propto \sin \theta$
$(4)$ Inversely proportional to the square of the distance $r$ of the point $P$ from the current element: $d B \propto \frac{1}{r^2}$
Combining these,$d B \propto \frac{I d l \sin \theta}{r^2}$,or $d \vec{B} = \frac{\mu_0}{4 \pi} \frac{I (d \vec{l} \times \vec{r})}{r^3}$.
Direction: The direction of $d \vec{B}$ is perpendicular to the plane containing $d \vec{l}$ and $\vec{r}$,determined by the right-hand rule.
Unit: The $SI$ unit of magnetic field is Tesla $(T)$. $1 \text{ Tesla} = 1 \text{ Weber/meter}^2$.