NMR and MRI Fields

Larmor Frequency

field sets resonance

NMR starts from a proportionality between magnetic field and resonance frequency. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A fixed nucleus has a field-frequency rule

This training model uses gamma 10 hertz per tesla. Real NMR uses real nuclear constants.

f=γB,γ=10f=\gamma B,\quad \gamma=10
Larmor proportionalityField strength and resonance frequency are paired by a training constant.fieldfrequency

A one-tesla field gives one checked frequency

Field 1 tesla gives frequency 10 hertz.

B=1 T⇒f=10 HzB=1\ \text{T}\Rightarrow f=10\ \text{Hz}
Larmor proportionalityField strength and resonance frequency are paired by a training constant.fieldfrequency

Doubling the field doubles the frequency

Field 2 tesla gives frequency 20 hertz.

B=2 T⇒f=20 HzB=2\ \text{T}\Rightarrow f=20\ \text{Hz}
Larmor proportionalityField strength and resonance frequency are paired by a training constant.fieldfrequency