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\section{The Biot-Savart Law}  Figure \ref{fig2} shows the contribution to the magnetic field \textit{d}$\vec{B}$ of each differential piece\textit{d}$\vec{l}$  of a current-carrying loop \textit{I}\textit{d}$\vec{l}$  of radius \textit{R}. 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 $\vec{B}$ in the $\hat{z}$ direction. Due to this cancellation we only want to integrate the upward components \textit{d}B_z \begin{equation}\label{eq1}  \vec{B}=\int{\textit{d}\vec{B_x}}