How does a tap to pay card work without battery?

Tap, beep, paid. But your bank card has no battery, nothing to charge, and it isn't plugged into anything. So where does the power come from? And how does a bit of plastic talk at all? Chapters 0:00 One little tap 0:32 A computer hiding in plastic 1:15 The invisible field 1:46 Power without a battery 2:22 Why so close? 3:05 Talking without shouting 4:00 A listening device from 1945 5:15 The secret the card never gives away 6:21 What does the beep actually mean? 6:56 Tapping your whole wallet 7:26 Why no PIN? 7:47 What about your phone? 8:25 One tap, broken down