Can you give some examples of vector precession equation dS/dz=ΩxS?

[andonrangelov]

Hi All,
I know that vector precession equations such as mdV/dt=qBxV (Newton's Second Law written for the magnetic part of the Lorentz force) exist.
In the last equation magnetic field B=(B1,B2,B3) acts as an effective torque and the speed V=(V1,V2,V3) is the “pseudo-spin vector”.
These equations can be written also as:

mdV1/dt=-qB3V2+qB2V3
mdV2/dt=qB3V1-qB1V3
mdV3/dt=-qB2V1+qB1V2

I know three applications of these equations:
1) Optical Bloch equations written for two-level atom;
2) Stokes equation of polarization optics;
3) Gyroscope precession


Can someone give other physical applications of the vector precession equation
(dS/dz=ΩxS)?

 

[AndyW]

Hi there,

There are actually many other physical applications of vector precession equations. Some examples include:

1) Particle accelerators: In particle accelerators, charged particles are accelerated by magnetic fields. The vector precession equation is used to calculate the trajectory of these particles as they move through the magnetic field.

2) Magnetic resonance imaging (MRI): MRI machines use strong magnetic fields to produce images of the human body. The vector precession equation is used to control the movement of protons in the body, which allows for the creation of detailed images.

3) Nuclear magnetic resonance (NMR) spectroscopy: NMR spectroscopy is a technique used to study the structure and dynamics of molecules. The vector precession equation is used to analyze the behavior of atomic nuclei in a magnetic field, which provides information about the structure of the molecule.

4) Magnetic levitation: The principle behind magnetic levitation, where an object is suspended in the air using magnetic fields, relies on the vector precession equation to control the movement of the object.

5) Magnetohydrodynamics (MHD): MHD is the study of the interaction between magnetic fields and electrically conducting fluids. The vector precession equation is used to model the behavior of these fluids in the presence of a magnetic field, which has applications in plasma physics and astrophysics.

I hope this helps expand your understanding of the wide range of applications for vector precession equations.