In a dynamo, how does current have enough time to flow through the wire if, in no time, it changes direction?

I had a lot of problems imaging the current in an AC generator.

I fully understand the principal of it and how it depends on a magnetic field repeatedly cutting another one and how to use Fleming’s right hand rule, I only still have trouble imagining why emf changes when the wire is in different positions.

Anyway it’s easy to imagine current changing direction when we are working with a single wire.

But in a dynamo it’s a rectangular coil/wire, and as it rotates at the same time the wire to the left will be cutting ,say, downwards the wire to the right will be cutting upwards.

So the way I wound up imagining it is sth like this: in a cross section of a wire electrons will be forced to flow in one direction then at the same time before they even flow away from the rectangular coil and to the rest of the wire to, let’s say, a lamp they will be pushed back to the opposite direction.