References / Physics and formulas

Field falloff with distance from a coil

Established physics
The report's default penetration estimates start from the on-axis field of a circular current loop, then fit a faster real-world falloff from the measured data.
Where it appears in the report: Penetration Depth Analysis

The evidence

The on-axis field of a circular loop falls off with distance in a way the loop's radius describes exactly. Real pancake and donut coils fall off faster than one ideal loop. So the report uses the loop formula only as a starting point, then fits an effective radius from a real measurement rather than assuming the ideal shape.
Field falling off with depth, fit to the dipole-loop modelA curve of field strength versus depth straight out from the coil. It starts at the surface peak and falls with depth along the on-axis dipole-loop model. A measured point is fit to the model to find the coil effective radius.100%50%10%Measured point, fit to the modelsurface1 R2 R3 RDepth into the body (multiples of coil radius R)Field strength (% of surface peak)© 2026 Gauss Labs
Straight out from the coil, the field falls off with depth along a known curve, the on-axis dipole-loop model. The report fits a single measured point to that curve to recover the coil effective radius, then uses the fitted curve to estimate how the field carries into the body. Real coils fall off faster than a single ideal loop, which the fit accounts for.

Primary sources

  • On-axis field of a circular current loop (Biot-Savart law); any introductory electromagnetics text.