Larmor Magnetic-Moment Precession

A classical unit spin S in a uniform magnetic field B = (0, 0, B) with normalized gyromagnetic ratio γ = +1 and magnetic moment μ = S experiences a torque τ = S × B. The dynamics are governed by dS/dt = S × B.

Experiment

Open Larmor Magnetic-Moment Precession to observe the dynamics interactively. Use these exact labelled controls to verify the classical precession properties.

1. Set Field B to 1, Tilt degrees to 45, Initial azimuth degrees to 0, and Time over pi to 0.5. Verify that Spin x is 0.0, Spin y is -0.7071, and Spin z is 0.7071.
2. Change Field B to -2. Verify that the rotation reverses direction, the signed precession frequency becomes 2, the final Spin x is -0.7071, and the final Spin y is 0.0. The magnetic energy becomes 1.4142.
3. Set Field B to 1, Tilt degrees to 45, Initial azimuth degrees to 90, and Time over pi to 0.5. Verify that Spin x is 0.7071, Spin y is 0.0, and the unwrapped phase is 0.0.
4. Set Field B to 0. Verify that the spin remains stationary at its initial position, with a precession frequency of 0 and magnetic energy of 0.
5. Set Field B to 1, Tilt degrees to 0, Initial azimuth degrees to 0, and Time over pi to 0.5. Notice that despite a formal precession frequency of -1, the spin is stationary pointing straight up with Spin z = 1.0.