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For example, the CGS volume magnetic susceptibility of water at 20 °C is 7.19 × 10 −7, which is 9.04 × 10 −6 using the SI convention, both quantities being dimensionless. Whereas for most electromagnetic quantities, which system of quantities it belongs to can be disambiguated by incompatibility of their units, this is not true for the ...
The magnetization field or M-field can be defined according to the following equation: =. Where is the elementary magnetic moment and is the volume element; in other words, the M-field is the distribution of magnetic moments in the region or manifold concerned.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In conventional NMR spectroscopy, T 1 limits the pulse repetition rate and affects the overall time an NMR spectrum can be acquired. Values of T 1 range from milliseconds to several seconds, depending on the size of the molecule, the viscosity of the solution, the temperature of the sample, and the possible presence of paramagnetic species (e.g ...
The spinning electron model here is analogous to a gyroscope. For any rotating body the rate of change of the angular momentum equals the applied torque : =. Note as an example the precession of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector ...
The magnetization is the negative derivative of the free energy with respect to the applied field, and so the magnetization per unit volume is = , where n is the number density of magnetic moments. [1]: 117 The formula above is known as the Langevin paramagnetic equation.
This effect is expressed on a macroscopic scale in the Einstein–de Haas effect, or "rotation by magnetization", and its inverse, the Barnett effect, or "magnetization by rotation". [1] Further, a torque applied to a relatively isolated magnetic dipole such as an atomic nucleus can cause it to precess (rotate about the axis of the applied field).
Crucially, the Larmor frequency is independent of the polar angle between the applied magnetic field and the magnetic moment direction. This is what makes it a key concept in fields such as nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), since the precession rate does not depend on the spatial orientation of the spins.