Ning Zhu edited subsection_Slope_Fit_Calculation__.tex  over 8 years ago

Commit id: 17c7b85cba5d96e2e90724cbdad2890574492cb4

deletions | additions      

       

\subsection{Slope Fit Calculation} From Figure \ref{fig:VB}  $$V=0.000443B+0.127$$  Therefore:  $$\frac{\Delta V}{\Delta B}=0.000443\frac{V}{mT}=0.443\frac{V}{T}$$  From Figure \ref{fig:directmethoddata}:   $$V=\frac{0.021\times (1+cos(\frac{2\pi\times(\theta-162)}{180}))}{2}$$  Taking the derivative at $\theta=117$ degrees:  $$\frac{\Delta V}{\Delta \theta}=\frac{0.21}{2}\times(-sin(2\frac{\pi}{180}(-45)))=0.21V$$  $$\frac{\Delta\theta}{\Delta B}=\frac{\Delta V}{\Delta B} \times \frac{\Delta \theta}{\Delta V}=0.443\frac{V}{T}\times\frac{1 radian}{0.21V}=2.1095\frac{radians}{T}$$  $$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1}\times2.1095\frac{radians}{T}=21.095\frac{radians}{T \cdot m}$$