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\section{The Biot-Savart Law}  The Biot-Savart Law relates shows how \textit{d}$\vec{B}$ depends on each differential piece of the current-carrying loop \textit{I}\textit{d}$\vec{l}$, the position vector $\vec{\textit{r}}$ of the point where we're finding the field, and the sine of the angle \theta between these two vectors with the equation:  \begin{equation}\label{eq1}  \texstit{d}\vec{B} = \frac{\mu_0}{4\pi} {\textit{I}\textit{d}\vec{l}\times\hat\textit{r}}{\textit{r^2}} \textit{I}\textit{d}\vec{l}\time\hat\textit{r}}{\textit{r^2}}  \end{equation}  The contributions to the magnetic field from the loop trace out a circle such that symmetrical horizontal components of the magnetic field cancel leaving a total field $\vec{B}$ pointing upward. Due to this cancellation we only want to integrate the upward components \textit{d}B_z