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Related Concept Videos

Atomic Nuclei: Larmor Precession Frequency01:11

Atomic Nuclei: Larmor Precession Frequency

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The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession,...
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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
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Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.
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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
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Consider an infinitely long straight wire carrying a current I. The magnetic field at point P at a distance a from the origin can be calculated using the Biot-Savart law.
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A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move perpendicular to it. If the field is in a vacuum, the magnetic field is the dominant factor determining the motion. Since the magnetic force is perpendicular to the direction of motion, a charged particle follows a curved path. The particle continues to follow this curved path until it forms a complete circle. Another way to look at this is that the...
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Related Experiment Video

Updated: Aug 24, 2025

Frequency Mixing Magnetic Detection Scanner for Imaging Magnetic Particles in Planar Samples
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Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution.

Anders Dyhr Sandgaard1, Noam Shemesh2, Valerij G Kiselev3

  • 1Center for Functionally Integrative Neuroscience, Department of Clinical Medicine, Aarhus University, Denmark.

NMR in Biomedicine
|October 26, 2022
PubMed
Summary

This study analyzes how magnetic tissue microstructure affects Larmor frequency shifts. Findings reveal optimal cavity sizes and a method to predict shifts based on cylinder orientation, improving magnetic property estimation.

Keywords:
Larmor frequencyLorentz cavitymagnetic microstructuremagnetic susceptibilitymodelingquantitative susceptibility mapping

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Area of Science:

  • Biophysics
  • Magnetic Resonance Imaging (MRI)
  • Materials Science

Background:

  • Magnetic susceptibility in tissues offers insights into composition and structure.
  • Current understanding of the link between magnetic microstructure and Larmor frequency shifts is limited to simplified models.

Purpose of the Study:

  • To investigate the relationship between mesoscopic magnetic microstructure and Larmor frequency shifts in biological tissues.
  • To develop analytical methods for predicting Larmor frequency shifts based on tissue microstructural organization.

Main Methods:

  • Computational simulations to analyze Lorentz cavities and inclusions in magnetized, NMR-invisible cylinders within an NMR-reporting fluid.
  • Analytical derivation of Larmor frequency shifts for populations of cylinders with varying orientation dispersion.

Main Results:

  • Optimal mesoscopic cavity size is approximately ten times larger than inclusion width for accurate analysis.
  • The Larmor frequency shift is determined by specific Laplace expansion coefficients of the cylinder orientation distribution function.

Conclusions:

  • Microstructural organization significantly influences measurable magnetic tissue properties.
  • Accurate estimation of magnetic properties requires detailed consideration of tissue microstructure and cylinder orientation.