# Drift Velocity

Did you know that, on average, the electrons in a conductor are randomly bouncing around at speeds of 10^5 m/s?

Yeah, it’s possible to compute using the formula: $v_{average}=\sqrt{\frac{3k_{b}T}{m}}$ replacing that lil “m” there with the mass of an electron, roughly m = 9.11 X 10^-31 kg. That “k” there is Boltmann’s Constant, and this result altogether comes from considerations of Thermal Mechanics with the Principle of Equipartition (which apparently is too over our heads to hear about in detail, but there ya go).

This random motion doesn’t mean there’s any net motion, i.e. Current.

No, rather, only once there’s a net motion of electrons in some direction (from one region to another) can we say that there’s a current flowing. This average velocity (10^5 m/s) is supplemented by another Drift Velocity that constitutes the current in any wire around!

Therefore: $v_{drift} = v_{average} + ({\frac{qE}{m}}) {\tau}$

Where that’s the same value for average velocity calculated before, and that “tau” is something called the Mean Free Time, essentially the average time between collisions (another thing from good ol’ Thermal Mechanics).

More explicitly (more accurately, rather): $v_{drift} = \sqrt{\frac{3k_bT}{m_{electron}}} + ({\frac{eE}{m_{electron}}})\tau$

Just leaving that “tau” a black box for now: if you’re interested, check out the post on Mean Free Time where there are some derivations available to ya. Treat yo’self!

In a wire you might find in your house, the Drift Velocity of the electrons can be fuckin slow as beans, like a few mm per second or something. Why does your lamp turn on “instantaneously”?

That’s because when the Circuit is completed, an Electric Field is “instantaneously” propagated through the conductive wire (in nature, it ain’t instantaneous baby, at best, like in this case, it’s at the Speed of Light).

That about sums up this concept, catch ya on the flip side!