= Solution
A <proton-precession magnetometer> measures the scalar magnitude $F=|\mathbf B|$ of the local <magnetic field>. Its sensor contains a proton-rich liquid, such as a hydrocarbon or suitable water-based fluid. A strong current through a coil briefly polarizes the nuclear <magnetic moments>, producing a small net <magnetization>. The polarizing field is directed sufficiently across the local <magnetic field> to leave a transverse component when the current is switched off.
The <protons> then undergo <Larmor precession> about the ambient <magnetic field>. Their rotating net <magnetization> induces a decaying alternating <voltage> in a receiving coil. Measuring the <frequency> determines the field:
$$
\omega=\gamma_pF,\qquad f=\frac{\gamma_p}{2\pi}F,\qquad \frac{\gamma_p}{2\pi}\simeq42.58\ \mathrm{MHz\,T^{-1}}.
$$
For example, $50\ \mathrm{\mu T}$ gives about $2.13\ \mathrm{kHz}$. The known proton <gyromagnetic ratio> provides an absolute frequency-to-field scale; this instrument does not measure the field's direction. Strong spatial <gradients> cause different parts of the liquid to precess at different rates and shorten the usable signal, which matters very close to a buried steel object.<G-857 Memory-Mag operation manual by Geometrics>[Introduction, “What is a total field magnetometer?”, and “Magnetic Environment”; scalar intensity and sensitivity to gradients.]{ref}
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