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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 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 B_z. B_z\hat{z}.  \begin{equation}\label{eq1}  \vec{B}=\int{\textit{d}\vec{B_x}}