The physics
A changing flux drives a current round a closed loop. Lenz's law gives its way: the current opposes the change that makes it.
ε = −dΦ/dt
A magnet coming toward a ring meets a like pole. So the ring pushes it back. A magnet going away meets an unlike pole, so the ring pulls it.
A loop moving away from a long wire loses flux. Its two sides along the wire both cut the field. The net emf is the difference of the two.
B = μ0I / 2πr ε = (Bnear − Bfar) ℓ v
A ring with no resistance keeps its total flux fixed. Its own flux L i changes to make up for the outside flux.
L i + B A = constant
Eddy currents flow in solid metal. A magnet falling down a copper pipe feels a drag F = k v. It soon falls at a steady top speed, m g / k. A metal disc under a circling magnet turns after it, a little slower.