Larson Lovdal edited section_The_Biot_Savart_Law__.tex  over 8 years ago

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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}}