Electron drift velocity

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Brewer
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Question asks:

A potential difference of 3.0V is applied to the ends of a copper wire which is 0.5m long. In copper at room temperature, the average time interval between collisions is [tex]\tau = 2.7*10^{-14}[/tex]s. What is the drift velocity of the free electrons in the wire?

Well, I know that [tex]V_{d} = \frac{eE\tau}{m}[/tex], but is E (electric field), just V/d? So it would be 6 (3/0.5)?

If it is that I thought that the electric field was radial due to the wire, and it seems to me that it should be along the wire for the electons to move.
 
V/L is the longitudinal electric field inside the wire and is responsible for exerting a force on a free electron, which is then accelerated along the length of the wire. Then obviously there will be interactions with the atoms in the material, which affect the path/motion of the electrons.

So yeah E = V/L
 
So what is the connection of the period(average time interval) between collisions on the problem?