I have a doubt about the understanding of drift velocities in a current. My problem is that the textbook speaks very loosely about this. It's like: "well, if we apply a field $E$ then the charges will experience a force due to this field, aquire acceleration, colide between then and because of that there will be a small resultant velocity for each particle called drift velocity".
But wait a moment, how can we be so sure of all of that? For me it's a little counterintuitive, and even if it was intuitive, how can we show that this really occurs? In other words, I feel that the first step to understand the meaning of drift velocity is to be really sure that this velocity will exist.
And once we've shown it exists, what's is this velocity anyway? Is the velocity of the particle in the direction of the current?
Thanks a lot in advance for your help!