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Ning Zhu edited subsection_Slope_Fit_Calculation__.tex
over 8 years ago
Commit id: 17c7b85cba5d96e2e90724cbdad2890574492cb4
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\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:
$$\frac{\Delta V}{\Delta \theta}=\frac{0.21}{2}\times(-sin(2\frac{\pi}{180}(-45)))=0.21V$$
$$\frac{\Delta\theta}{\Delta B}=\frac{\Delta V}{\Delta B} \times \frac{\Delta \theta}{\Delta V}=0.443\frac{V}{T}\times\frac{1 radian}{0.21V}=2.1095\frac{radians}{T}$$
$$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1}\times2.1095\frac{radians}{T}=21.095\frac{radians}{T \cdot m}$$