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Electrical EngineeringQ&A LibraryProblem 3.4 A static field points uniformly along the positive z-axis. A classical spinning par- ticle, with positive gyromagnetic ratio y and fixed magnetic moment magnitude , has its spin initially in the direction of the static field. A circularly polarized rf field points along the axis with time-dependent amplitude Big/(t) (e.g., the rf field may be turned off at a later time) applied on-resonance starting at t 0. a) Give expressions analogous to (3.33) for all three magnetic-moment vector components in the rotating (prime) reference frame for time t > 0. Your answer will be in terms of a definite integral b) Show that the equation of motion (2.24) is satisfied by your answers in (a) for BBly c) Find the generalization of (2.35) needed for this time-dependent case. dt2 (2.35) dt2Start your trial now! First week only $4.99!*arrow_forward*

Question

textbook: Magnetic resonance imaging, physical principles and sequence design.

Problem 3.4

eq 3.33 : μx′(t) = μx′(0)

μy′(t) = μy′(0) cos φ_{1}(t) + μz′(0) sin φ_{1}(t)

μz′(t) = −μy′(0) sin φ_{1}(t) + μz′(0) cos φ_{1}(t)

eq 2.24: d~μ/dt

= γ~μ × ~B

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