deletions | additions       diff --git a/subsection_Varying_the_Polarization_time__.tex b/subsection_Varying_the_Polarization_time__.tex  index 8418e0f..fa7a919 100644  --- a/subsection_Varying_the_Polarization_time__.tex  +++ b/subsection_Varying_the_Polarization_time__.tex 
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\subsection{Varying the Current}   The relationship described in Eq. \ref{eq:growthrate} can not be applied to the degree of polarization or magnetization. In order to determine whither whether  the degree of polarization depends on the strength of magnetic field, we have to vary the current. When varying the current, for electronic systems the fractional populations is effected by the g-factor or the spectroscopic splitting factor. This causes and lower and upper state, where $N_1$ represents the lower state and $N_2$ represents the upper state. The difference between these two states multiplied by the magnetic moment describes the magnetization of the field. The following relationship can be expressed in the equation below \textbf{(cite textbook)}, \begin{equation}   \label{eq:tanh}  M=(N_1-N_2)\mu= N\mu\cdot\frac{e^x-e^{-x}}{e^x+e^{-x}}=N\mu tanhx  \end{equation}  Theory %Theory  predicts that magnetization follows the relationship described in Equation \textbf{(insert eqn)} because magnetization is effected by quantum factors within the atom as well as the applied magnetic field, so it cannot be as simply modeled by an exponential. \\ \\ \subsection{Studying Larmor precession}  Larmor precession is when a proton in a magnetic field experiences a magnetic torque that aligns the proton magnetic moment with the field. Due to the angular momentum and spin, the proton's motion is a precession about the magnetic field. Taking $B_{e}= \text{Earth's magnetic field} \approx 50 \mu T$ and $\gamma= 2.675 \cdot 10^8 \frac{1}{s\cdot T}$, mathematically the precession frequency would be around,