Alisha Vira edited basic_equations_and_physics_The__.tex  over 8 years ago

Commit id: 3a0df95d4aae09d7364861f39df375c51fc79500

deletions | additions      

       

basic equations and physics \\   The relationship between the polarization time and the voltage is described by the growth rate. The growth rate of M(t) towards $M_{\infty}$ is described by the following equation,   \begin{equation}  \label{eq:growthrate}  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). \\ \\  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,