this is for holding javascript data
Larson Lovdal edited section_The_Biot_Savart_Law__.tex
over 8 years ago
Commit id: 88c1d5b50a864874f9740de1919f61a9f51aa2df
deletions | additions
diff --git a/section_The_Biot_Savart_Law__.tex b/section_The_Biot_Savart_Law__.tex
index a7ba182..1e66fc6 100644
--- a/section_The_Biot_Savart_Law__.tex
+++ b/section_The_Biot_Savart_Law__.tex
...
\begin{equation}\label{eq1}
\textit{d}\vec{B} = \frac{\mu_0}{4\pi} \frac{\textit{I}\textit{d}\vec{l}\times \hat{\textit{r}}} {\textit{r}^2}
\end{equation}
The contributions to the magnetic field from the loop trace out a circle thus the symmetrical horizontal components of the magnetic field cancel leaving a total field $\vec{B}$ pointing upward. Due to this cancellation we only want to integrate the upward components \textit{d}$B_z$. We can isolate these components using \textit{d}$\vec{B}_z =
\textit{d}\vec{B}\cos{\theta}$ \textit{d}\vec{B}\cos{\theta}$, which comes from the right triangle in the top of figure \ref{fig2} formed by \textit{d}$\vec{B}$, $\vec{B}$, and the radius of the circle.
\begin{equation}\label{eq2}
\vec{B}=\int{\textit{d}\vec{B_x}}