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Ning Zhu edited subsection_Slope_Fit_Calculation_From__.tex
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\subsection{Slope Fit Calculation}
\begin{eqnarray}
From Figure \ref{fig:VB}
$$V=0.000443B+0.127$$ $$V&=&0.000443B+0.127$$\\
Therefore:
$$\frac{\Delta V}{\Delta
B}=0.000443\frac{V}{mT}=0.443\frac{V}{T}$$ B}&=&0.000443\frac{V}{mT}=0.443\frac{V}{T}$$\\
From Figure \ref{fig:directmethoddata}:
$$V=\frac{0.021\cdot (1+cos(\frac{2\pi\cdot(\theta-162)}{180}))}{2}$$ $$V&=&\frac{0.021\cdot (1+cos(\frac{2\pi\cdot(\theta-162)}{180}))}{2}$$\\
Taking the derivative at $\theta=117$ degrees:
$$\frac{\Delta V}{\Delta
\theta}=\frac{0.21}{2}\cdot(-sin(2\frac{\pi}{180}(-45)))=0.21V$$ \theta}&=&\frac{0.21}{2}\cdot(-sin(2\frac{\pi}{180}(-45)))=0.21V$$\\
$$\frac{\Delta\theta}{\Delta
B}=\frac{\Delta B}&=&\frac{\Delta V}{\Delta B} \cdot \frac{\Delta \theta}{\Delta V}=0.443\frac{V}{T}\cdot\frac{1
radian}{0.21V}=2.1095\frac{radians}{T}$$
$$V_{c}=\frac{1}{L}\cdot radian}{0.21V}=2.1095\frac{radians}{T}$$\\
$$V_{c}&=&\frac{1}{L}\cdot \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1}\cdot2.1095\frac{radians}{T}=21.095\frac{radians}{T \cdot m}$$
\end{eqnarray}