Ning Zhu edited subsection_Slope_Method_The_direct__.tex  over 8 years ago

Commit id: 91032543303ecfcefae7e730998b695514691c34

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%We got 45 degrees after applying trigonometry to our previous fits since we used $cos$ function instead of $cos^2$ to fit our data in \ref{fig:directmethoddata}.   %which is the point of inflection on the $V$ vs $\theta$ graph.   %This value is consistent with the value we got when we set the second derivative of $\frac{V}{\theta}$ to zero (the inflection point).   To verify the value of the Verdet constant, we used a second method where the polarizer stayed at the angle of greatest sensitivity, which is 45 degrees after we applied trigonometry to our previous fits. We did this because we used $cos$ function instead of $cos^2$ to fit our data in Figure  \ref{fig:directmethoddata}, but we will be expressing $V(\theta)$ in the form of $cos^2$ in the rest of our report. %We got the angle by setting the second derivative of $\frac{dV}{d\theta}$ to zero, which corresponds to the inflection point.  We then varied the current of the solenoid, going in 0.5A steps from -3A to 3A, thereby varying the magnetic field within the solenoid between -33.3 mT and +33.3 mT. We could then graph voltage vs magnetic field, which results in a linear graph as shown in Figure \ref{fig:VB}. The slope of the graph is $\frac{\Delta V}{\Delta B}$. We calculated $\frac{\Delta V}{\Delta \theta}$ previously, so we can find $\frac{\Delta B}{\Delta\theta}$ and therefore the Verdet constant.