MRI Gradient-Frequency Three-Row Scan - Physics for Biophysics Step by Step

A steeper ideal gradient maps the same far position to a larger frequency code. 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 far sample is the clearest gradient check

Base field stays 1 tesla. The table watches the sample at 2 meters as the gradient index changes.

B(z)=B_{\text{base}}+Gz,\quad f=\gamma B

A steeper gradient makes a higher frequency code

The far-position field and frequency both rise row by row. This is still a one-dimensional training model, not a full MRI pulse sequence.

\begin{array}{c|c|c}G&B_{\text{far}}&f_{\text{far}}\\1&3\ \text{T}&30\ \text{Hz}\\2&5\ \text{T}&50\ \text{Hz}\\3&7\ \text{T}&70\ \text{Hz}\end{array}

The rendered row maps two meters to fifty hertz

With gradient index 2, the far field is 5 tesla and the frequency code is 50 hertz.

5\ \text{T}\cdot10\frac{\mathrm{Hz}}{\mathrm{T}}=50\ \text{Hz}