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Ning Zhu edited Figures.tex
over 8 years ago
Commit id: 509dbf3989a6ca14c8b184923f7915f0b98111f8
deletions | additions
diff --git a/Figures.tex b/Figures.tex
index f99c86a..a9c48e3 100644
--- a/Figures.tex
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...
$$\Delta\theta=\theta_{B}-\theta_{0}=-0.069 radians$$
$$\Delta B=-3A\times 11.1\frac{mT}{A}=-33.3mT$$
$$\frac{\Delta\theta}{\Delta B}=\frac{-0.069radians}{-33.3mT}=0.00207\frac{radians}{mT}=2.07\frac{radians}{T}$$
$$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1m}\times
2.07\frac{radians}{T}=20.7\frac{1}{T*m}$$ 2.07\frac{radians}{T}=20.7\frac{radians}{T*m}$$
2. Slope Fit
As shown in Figure 2:
...
$$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$$
\frac{\Delta\theta}{\Delta B}=\frac{\Delta V}{\Delta B} \times \frac{\Delta \theta}{\Delta V}=0.443\frac{V][T}\times\frac{1 radian}{0.21V}=2.1095\frac{radians}{T}$$
$$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1}\times2.1095\frac{radians}{T}=21.095\frac{radians}{T*m}$$