A linear field gradient turns position into a distinguishable resonance frequency: adding Gz to the base field B0 shifts each spin's frequency by an amount set only by where it sits along the line. With the schematic gamma = 10 Hz/T used here (not water's real ~42.58 MHz/T proton ratio) and a 1 T/m gradient, positions 0 m, 1 m, and 2 m give three exactly evenly-spaced frequencies — the mechanism a real scanner exploits to read spatial position from a frequency spectrum, though actual hardware also needs a receiver bandwidth and Fourier transform that this toy ledger does not model.
A one-dimensional MRI gradient maps position to 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
The gradient changes field by position
The field values are 1 T, 2 T, and 3 T in this one-dimensional training line.
B(z)=B0+Gz
Frequency follows field
With gamma 10 Hz/T, the frequencies are 10 Hz, 20 Hz, and 30 Hz. The gamma value is schematic, not a real nuclear constant.