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Emily A Kaplan edited The_relationship_between_the_polarization__.tex
over 8 years ago
Commit id: e5bfe1712210eaceeefb56494cd87ecb8ff61900
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M(t)=M_{\infty}(1-e^\frac{t}{T_1})
\end{equation}
However, the same relationship described in Eq. \ref{eq:growthrate} can not be applied to the degree of polarization (or the magnetization).
\\ 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. \textbf{(cite textbook)}\\
\\
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,
\begin{equation}