I need to use the following equation (Bio-Savart) of a wire carrying a current, where $d\vec l$ is an infinitesimal piece of wire carrying the charge (the thicker line, half circle)
:
$$d\vec B=\frac{\mu_0I\left(d\vec l \times \vec r\right)}{4\pi (|\vec r|^3)}$$
Where $\left(d\vec l \times \vec r\right)$ is the cross product of $\vec r$ and $d\vec l$.
Now $\vec r=r\sin\theta \hat x +r\cos\theta\hat y $ since we're going clock-wise, but what would I use as $d\vec l$?