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How to use
Pick a preset or set latitude and longitude to move the observer; drag to orbit the globe. The compass dial shows the declination and horizontal strength; the cross-section shows your site on the magnetic meridian plane with the local field vector (the dip). Change the pole latitude and longitude to tilt the dipole, or fade the dipole strength to mimic a reversal. Space pauses, R resets.
Models and baked PBR textures (continents are procedural, not real coastlines) made in Blender; Three.js r160 draws the field lines from the same dipole module as the 2D page.
The science
To a good first approximation Earth's main field is a geocentric dipole tilted a few degrees from the rotation axis. In SI units, with moment m and position r (distance r from the centre):
B(r) = (mu0/4pi) [ 3 (m.r^) r^ - m ] / r^3 B0 = mu0 M / (4 pi Re^3) = 29.4 uT (equatorial surface value, dipole fit)
Here m points towards the geographic south side of the planet, so the field leaves the surface near the south magnetic pole and enters near the north geomagnetic pole (80.7 N, 72.7 W in this model). With magnetic latitude λm the field components are B_horizontal = B0 (Re/r)³ cos λm and B_vertical = 2 B0 (Re/r)³ sin λm, so
F = B0 (Re/r)^3 sqrt(1 + 3 sin^2 lm), tan I = 2 tan lm, field lines: r = L Re cos^2 lm
The 2D page maps and the 3D globe show the vector into the usual geomagnetic elements: X north, Y east, Z down, H = sqrt(X²+Y²), F total, inclination (dip) I = atan(Z/H) and declination D = atan(Y/X), the angle between a compass needle and true north. The dip is what lets sea turtles, birds and compasses read latitude; the needle becomes unusable where I approaches 90 degrees.
Honest simplifications. This is a pure tilted dipole. The real field (IGRF) adds non-dipole terms: for example, London's real declination is about 0 degrees and F about 49 uT, while this model gives roughly -15 degrees and 50 uT, and the dip at the real equator wanders off the dipole line by several degrees. Solar-wind compression, crustal fields and secular variation are ignored. The "dipole strength" slider scales the whole field to show how it fades during a reversal; real reversals are not simple scalings (the field becomes multipolar). Pole position and strength defaults are rounded values for the early 2020s.
Numerical checks below test the code against closed forms and against Maxwell's equations outside the sources: the divergence and curl of B must vanish (central differences), the equator gives B0, the pole 2 B0, the inclination follows tan I = 2 tan lm and the field falls as r^-3.