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Larson Lovdal edited We_can_isolate_the_components__.tex
over 8 years ago
Commit id: a1e1f2ade07c0dd649ea85b323eac95f00272458
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\end{equation}
We can further simplify equation \ref{eq4} by making two careful choices about the experimental setup. First, we choose to investigate the point exactly halfway between the coils, as shown in Figure \ref{fig1}, such that $\textit{z}=\frac{\textit{d}}{2}$. Second, we set the coils such that the separation distance \textit{d} is the same as the radius \textit{R}. The denominator of equation \ref{eq4} then becomes $(\textit{R}^2+(\frac{\textit{R}}{2})^2)^\frac{3}{2}$. Substitutting back into equation \ref{eq4} and canceling we arrive at our final expression for the magnetic field at the center of the Helmholtz configuration:
\begin{equation}\label{eq5}
B=5 B=\frac{8\mu_0\textit{N}\textit{I}}{\sqrt{125}\textit{R}}
\end{equation}