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Larson Lovdal edited section_The_Biot_Savart_Law__.tex
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\section{The Biot-Savart Law}
Figure \ref{fig2} The Biot-Savart Law relates shows
the contribution to the magnetic field how \textit{d}$\vec{B}$
of depends on each differential piece of
a the current-carrying loop
\textit{I}\textit{d}$\vec{l}$ \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
radius \textit{R}. the angle \theta between these two vectors. 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. pointing upward. 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}}