My girlfriend has an electric bike (tasman cruiser) and I think there are many similar ones out there (they are chinese mostly made and there arent really any high or low spec ones they are all pretty basic). Basically it is magnetically driven by the back wheel hub. This is the best setup because you have the freedom to simply cycle unassisted, have partial assistance or dont bother pedaling at all! It runs of a large lipo battery which is the most expensive part of the bike. It needs to be handled with care and, if you use the cycle alot you should be prepared for the fact that it will need replacing after a couple of hundred charges.
This particular model cannot be described as a mountain bike and the frame shape is kind of old fasioned but considering the fact that the added weight of the battery and cheap frame will make anything but road use impossible you shouldnt be fooled into buying a more expensive bike just because it has a more modern mountain bike look. £600 got the bike battery and a child trailer which our son LOVES!
It rides nicely and can get some nice speed up in full electric mode. Very steel hills will most likely require the assistance of the pedals too, especially if using a trailer. Battery time varies and with most of these bikes the battery is the most expensive part so make sure you check the capacity rating of the battery to ensure you get the highest possible.
Hope you find something good.