Ning Zhu edited subsection_Slope_Fit_Calculation_begin__.tex  over 8 years ago

Commit id: 7bda6804424887ab9d6d1fe0d673cc005a6621d4

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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:  $$\frac{\Delta \frac{\Delta  V}{\Delta B}&=&0.000443\frac{V}{mT}=0.443\frac{V}{T}$$\\ 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:  $$\frac{\Delta \frac{\Delta  V}{\Delta \theta}&=&\frac{0.21}{2}\cdot(-sin(2\frac{\pi}{180}(-45)))=0.21V$$\\  $$\frac{\Delta\theta}{\Delta \theta}&=&\frac{0.21}{2}\cdot(-sin(2\frac{\pi}{180}(-45)))=0.21V\\  \frac{\Delta\theta}{\Delta  B}&=&\frac{\Delta V}{\Delta B} \cdot \frac{\Delta \theta}{\Delta V}=0.443\frac{V}{T}\cdot\frac{1 radian}{0.21V}=2.1095\frac{radians}{T}$$\\  $$V_{c}&=&\frac{1}{L}\cdot radian}{0.21V}=2.1095\frac{radians}{T}\\  V_{c}&=&\frac{1}{L}\cdot  \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1}\cdot2.1095\frac{radians}{T}=21.095\frac{radians}{T \cdot m}$$ m}  \end{eqnarray}