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Is the US finally getting ‘all aboard’ with electric trains?
(www.theverge.com)
This is a most excellent place for technology news and articles.
The best use of a battery on a train is a small one to handle junctions. You disconnect from the wire at the end of one set, go through the junction, and then reconnect at the other side. Saves a lot of ugly spaghetti wiring.
Otherwise, no, just use wires.
You don't even need that. Every electric train I know of has pickups on each car, and any break in the catenary or third rail is short enough that it can be bridged naturally by two cars, or sometimes even just one, if it has pickups at both ends.
Some electric trolleys aren't long enough to do that.