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\begin{equation} \left.\frac{dV_{\mathrm{pd}}(B)}{dB}\right|_{\textrm{max}}=\left.\left(\frac{dV_{\mathrm{pd}}}{d\phi}\right)\right|_{\pi/4}\left(\frac{d\phi}{dB}\right)=-\left(V_{0}\left.\sin[2\phi]\right)\right|_{\phi=\pi/4}v_{c}L.\\ \end{equation}

This data was then plotted with Voltage(photodiode) on the y axis, and Magnetic Field on the x axis, which you can see in Fig. \ref{fig:MethodTwoGraph}. A linear fit was applied to the graph to obtain \(dV_{pd}(B)/dB\), and \(dV_{pd}/d\phi\) was found evaluating Eq. \ref{eq:Simplifed_Diode_Response_Equation} at \(\phi=\pi/4\), which is just \(-V_{0}\). Using Eq. \ref{eq:13}, we calculated \(v_{c}\).

Note that since we are changing the \(\vec{B}\), if you are using a solenoid as the source of magnetic field, beware of the limit of the current that is allowed for the solenoid.

It came to our attention as we were collecting data that there is a difference in the rate of change of \(V_{pd}\) with respect to \(\vec{B}\) between sweeping up and sweeping down the field. The cause of such needs to be further investigated, but in this experiment, we used the sweep up data for its consistency over several measurements, and consistency with the other two methods.