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\section{The Biot-Savart Law}  \ref{fig2} shows the contribution \textit{d} \vec{B} \textit{d}$\vec{B}$  to the magnetic field of each differential piece \textit{d} \vec{l} \textit{d}$\vec{l}$  of a current-carrying loop of radius \textit{R}}. We can see in \ref{fig2} that the contributions to the magnetic field from the loop traces out a circle  \begin{equation}\label{eq1}