Very long cables at normal supply voltages (240V/380V) suffer too much voltage drop over any distance (say) >150m. Remember that we're talking of multi-kilometre distances, not a mere hectare or two.Not only that, but anyone who has used an electric lawnmower on a larger area will tell you that cables are a fucking hazard to navigation when you're trying to move a machine trailing a cable. They constantly get tangled, driven over and cut.So anything at a reasonable voltage to run heavy machinery at a long distance from the nearest supply would need to be... I don't accurately know -- ask an electrical engineer for a definitive answer, but... something like 1.1kV. Cable that's sufficiently well insulated for moderately high voltage is /very/ expensive and deadly if the insulation gets compromised. Doesn't sound very feasible to me. Maybe someone with more EE knowledge can prove me wrong -- this is just my gut-feel conjecture. I got kicked out of the EE program at university for being bored to tears by this sort of stuff.

 We run trains over multiple kilometres with overhead wires why can’t we do it with tractors???
 >why can’t we do it with tractors???Trains run in straight lines, farm equipment has various widths and it's not just 'tractors' and you're going up and down rows of farmland that might be tens or hundreds of acres wide and that aren't always in the shape of a square or rectangle (it's often far easier to work around large glacial boulders or trees for example, as well as ditches/running water/property lines etc). You'd have to string millions and millions, if not billions and billions, of miles of electrical cable across fields.There's 915 million acres of active farmland in the U.S., that's 1.4 million square miles/3.7 million square kilometers. The larger combines can be about 40ft wide so if every scrap of farmland was in literally-square acre parcels you're going to need 5.2 power lines minimum to cover the width of a literally-square acre so you're easily talking 5 million miles of power lines.
 You could, but it would be cost prohibitive in a real economic sense.You run overhead wires where you know you will repeatedly have a large demand for power, and you pay for it once in the capital outlay to put up the wires and other scaffolding.In other words, you want to do this where (average demand / (fixed capital cost (which correlates to peak demand)) is relatively high. The middle of the farm field is the exact opposite of that: power demand is bursty and very infrequent, so utilization will be a few orders of magnitude lower.
 Trains are linear. Tractors and harvesters are areal.You square the delivery line requirement.A 1,000 km electric traction rail line needs 1,000 km of cable. (Or 2,000 km for a two-tracked system.)A 1,000 km * 1,000 km area of farmland with power gridded every 100m has 10k * 10k or 100,000,000 km of delivery cable.

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