Built on Facts

Drift velocity

Driving in my car for five hours today, I had plenty of time to think about velocity. There’s not much you can do about it, speeding doesn’t take much time off the trip but it does add the risk of an expensive ticket. We single classical particles don’t have a lot of options for getting from place to place very quickly.

The situation is a little more interesting with flows of current. If you want to fill a large bucket with water from a garden hose at one cubic foot per second, the hose is going to have to be turned on very high. Water will be flying out of the end of the hose at some preposterous speed. On the other hand, the Mississippi River can deliver more than half a million cubic feet of water per second with the water flowing at a walking pace. The power of the current doesn’t just depend on the speed of the flow.

Electricity is like that as well. 1 ampere of current is a fairly typical value for the flow through an incandescent light bulb. That much current corresponds to a flow of 6 million trillion electrons per second. It’s a lot, but electrons are very tiny. To find out how fast the electrons are moving, we need the following formula:

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Where I’m using the slightly non-standard notation that I is the current in electrons per second, rho is the density of electrons in the wire, and A is the cross-sectional area of the wire.

But we don’t know what the density – how many conduction electrons per cubic meter – there are in the wire. It’s actually a fairly delicate experiment to find out, but it has been done. The density of conduction electrons in something like copper is huge. It’s on the order of 8e28 per cubic meter. Plugging that into our equation with some typical wire values gives a drift velocity of a fraction of a millimeter per second. The electrons in your wires are moving pretty slowly.

Then how does a light turn on so quickly when you hit the switch? Like the water in a garden hose, the wire is already filled with electrons. The pressure causes them to all start moving, and the ones already at the bulb being to be pushed through, causing light. It’s along the same lines as how there’s a delay between turning on the hose and the water coming out only if the hose starts off empty. If there was already water in it, the flow begins almost immediately.

Comments

  1. #1 Uncle Al
    March 16, 2009

    If the water hose is filled, the new information will propagate no faster than local soundspeed and be further slowed by hose wall elasticity. You could put through a shock for faster connection (e.g., water hammer in rigid piping) but not overall volume flow. The wire signal will not be faster than lightspeed attenuated by the square root of local dielectric constant and square root of magnetic interaction. Look at twisted pair, ladder, and coax configurations. Foamed polyethylene insulator coax is faster than solid polyethylene insulator coax. Refractive index (distant from an optical transition) rises with polarizable ions or atoms (e.g., Pb+2 “crystal”; organic pi systems) and with magnetic ions (lanthanide glasses being a pleasant surprise for optical train designers around the U-2 flying).

    Engineer – to intentionally design with efficiency.

    Diamond has a large refractive index with only light element singlet sigma bonding. Huge optical rotations can be obtained without chromophores in strictly aliphatic homocyclic systems. Engineer to keep your job, then add beauty to steal somebody else’s.

  2. #2 Paul Murray
    March 16, 2009

    Household electricity is AC (50 Hz here in Oz), so the electrons are just moving back and forth in the filament by a 50th of a fraction of a milimetre or so.

  3. #3 John-Michael Caldaro
    March 17, 2009

    My assumption is that this is the average velocity of the large group of electrons much the same way the temperature of a group of atoms or molecules is the average KE of those particles. In addition I am assuming that this value is true for both AC and DC. What about the long term drift velocity for DC current. Is that dependent on amount of current flow?

  4. #4 John-Michael Caldaro
    March 17, 2009

    Oops. I meant that the average velocity of atoms is related to the average KE of the atoms or molecules.

  5. #5 rob
    March 17, 2009

    the motion of electrons in a metal with an applied field is the superposition of two velocities. there is the velocity of the electrons due to their kinetic energy (large) and the velocity of the electrons due to the applied field (very small).

    the expression for drift velocity that Matt wrote above is for the small velocity superimposed on the large velocity due to kinetic energy (also called Fermi velocity.)

    check this site out for a picture:

    http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/ohmmic.html

    one question you may want to think about is why is the drift velocity a constant? howcome the electrons don’t just keep accelerating due to the force from the electric field?

  6. #6 pin
    April 23, 2011

    Hai…

    Can we find the standard/theoretical value for metal such as copper or tantalum

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