Example 1.1 B. z Consider the case in which B is along the z direction and /4 is initially at an angle of e to B and in the xz plane (see Fig. 1.4). Then Mix = y Buy (1.7) Hy = -y Bux (1.8) Hz = 0. (1.9) so that & is constant with time and /, and uy both oscillate. Solving these Fig. 1.4 A magnetic moment fe in a magnetic differential equations leads to field B precesses around the magnetic field at the Larmor precession frequency, y 8. where ux (!) = \\/| sine cos(wit) (1.10) y is the gyromagnetic ratio. The magnetic field B lies along the z-axis and the magnetic My (!) = lusine sin(ant) (1.11) imoment is initially in the x2-planc at an an- "= (1) = lu| cose. (1.12) gle o to B. The magnetic moment processes around a cone of semi-angle a. where an =yB (1.13) is called the Larmor precession frequency. Joseph Larmor (1857-1942)