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Nathanael A. Fortune added subsection_Varying_the_Current_The__.tex
over 8 years ago
Commit id: ad34acf567c1a74319c48431dbbda8a0366d81b1
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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 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 are affected 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 \cite{Kittel_1953},
\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 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.
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