Or a coil in the battery case otherwise you'd have to charge it on the bike, I can't imagine that the convenience is worth the extra weight, cost and charging time. Plus people who carry their charger with them will have double the extra weight to carry.Just install maglev. Then we can do away with tyres, pothole repairs and gritting. Or vacuum tubes that you ride in! They've already got vacuum waste systems across whole cities.
Induction charging will be a big thing over the next few years for consumer electronics. dell already have a laptop with an induction charger and I've seen a video where the charger is on the floor and the laptop on the desk.
Induction charger will add to weight a bit because you'll need a coil on the bike.