Dependence of magnetization (proton density, field strength and temperature)

Last revised by John David Mayfield on 12 Oct 2021

The dependence of magnetism is based on proton density (PD), field strength and temperature. There is a frictional interchange of energy between the protons and the lattice (spin-lattice interaction), such that a balanced exchange occurs between the two energy states and the thermal equilibrium is established. Thermal equilibrium occurs when the net number of transitions between the two energy states is zero. The relative population of the two states is determined by the value of the external magnetic field and the lattice temperature.

At any one moment in time, a slight excess of nuclei has their magnetic moments aligned parallel with the main magnetic field (B0), i.e. in spin-up (lower energy) states.

The resultant equilibrium magnetization (M0) becomes aligned with the external field (B0), producing a net magnetic effect called net magnetization vector (NMV), given by:

  • M0 = (γ2 h2 B0 Ntotal) / (16 π2 kT)
  • γ = 42.58 MHz/T for hydrogen
  • h = Planck's constant (6.62607004 x 10-34 m2 kg s-1)
  • k = Boltzmann's constant (1.38064852 x 10-23 m2 kg s-2 K-1)
  • T = absolute temperature (310 K at room temperature)

The magnitude of net magnetization (M0) is directly proportional to proton density (N) and magnetic field strength (B0). As the magnitude of the external magnetic field increases, more of the magnetic moments of the nuclei line up parallel to the field (because the amount of energy required to oppose the field is higher). That is to say, the low energy population increases and the NMV gets larger.

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