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.
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 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.
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.
Agricultural land is typically in remote areas, and equipment needs to be driven for miles often to get to where it's being used.
Even if, lets say you do take the hit of the upfront costs introduce a heavy-duty power-grid to service all your land (thousands of hectares on many of the large-scale cases) - then you're still going to have to run the cable from some kind of power point, and without some aerial apparatus you're going to be running it across and through your crops.
Yeah I guess you could take the time to arrange the cable, and have somebody follow it around all day but that's a lot of extra work. Probably a lot more work than just the harvesting.
It's probably pretty dangerous too - trailing this multiphase high-power cable around where you've all this heavy equipment often doing chopping and grinding.
If this is possible at all, it could be an important base technology for a very wide range of new application fields.
The kind of heavy duty cabling you're talking about would be very very heavy.
Now, you're not only talking about powering your combine harvester or whatever but also an army of heavy duty drones?
LOL
I want to add that for farm equipment, having a big weatherized battery cube and a crane to swap it is practical. For automobiles, less so.