Larmor Equation

For a particular magnetic field strength, the (resonant) frequency of precession can be calculated via the Larmor equation. The Larmor equation may be derived using classical physics or quantum mechanics. It links these two descriptions of nuclear magnetic resonance, and is fundamental to MRI physics. The Larmor equation is

ω₀ = γ B₀

where ω₀ is the angular frequency of precession of protons in an external magnetic field, γ is a proportionality constant called the gyromagnetic ratio, and B₀ is the strength of the external magnetic field. γ = 2.67*10⁸ radians s^-1 T^-1. In some texts the right-hand side of the equation is negative; this simply depends on the direction in which a positive rotation is defined.

We may also write f₀ = γ B₀, where γ = 42.56 MHz T^-1 (γ = γ/2π).

Example: the Larmor frequency f₀ for a 1.5 T magnet is 1.5(T)*42.56(MHz T^-1) = 63.8 MHz.