A geomagnetic storm drives current through any long grounded conductor — a telegraph line in 1859, a transmission line today. Everyone says long lines are the problem. Drag the length slider and watch what actually happens.
the storm's electric field E acts along the line; the circuit closes through the earth at both ends
What the shape is telling you. The storm's voltage
E·L grows without limit as the line gets longer — that part of the folk story is
right. But the line's own resistance r·L grows at exactly the same rate. Divide one
by the other and the length cancels: past a few tens of kilometres the current flattens onto
E/r and stays there.
So the vulnerable quantity is not length. It is ohms per kilometre — and that is the number transmission engineering has spent a century and a half driving down, because resistance per kilometre is also what wastes power. A 4 mm iron telegraph wire is about 8 Ω/km. A modern aluminium conductor is about 0.06 Ω/km. Same storm, same formula, roughly 130× the current.
Assumptions, so you can disagree with them. Single conductor grounded at both ends, uniform field along the line, quasi-DC so inductance is ignored, and earth resistance treated as a lumped value per end. A real grid is a mesh with transformer windings and many grounds, so treat the modern numbers as an order of magnitude and not a load-flow result. Resistances here are computed from resistivity and cross-section: iron 1.0×10⁻⁷ Ω·m, aluminium 2.82×10⁻⁸ Ω·m.