What is the speed of electrons in a copper wire, used to charge a device? If there is a fixed speed, how is it determined?
There is no point in speaking about the "speed of an electron in a copper wire". You may ask the drift velocity of the electron under an applied potential. The electrons are randomly scattered by phonons (lattice vibrations) as well as the metal ions. Under an applied field, in addition to the thermal random motion, the electron moves from region of negative potential to the region of positive potential with an average velocity, a motion which is known as drift. The drift velocity of an electron is very low: about $1 mm/s$. However, the Fermi velocity is as higher as several ten or hundred thousands of meters per second for a metal. The drift velocity of an electron in a metal is given by
where $e$ is the electronic charge, $m$ is the electron rest mass, $E$ is the applied electric field and $\tau$ is the relaxation time.
To know the drift velocity of electrons in copper, all you have to do is just measure the resistance of copper.
Then the conductivity of copper is given by
where $R$ is the resistance of the copper wire, $l$ and $A$ are the length and cross-sectional area of the wire. If the applied potential difference across the length of the wire is $V$, then the electric field can be approximated as
Now, the Fermi velocity of copper can be found out if you know the Fermi energy of copper ($7.00 eV$):
Next, you need the mean free path length, which is given by
where, $n$ is the electron density in copper, and is given by
where, $N_A$ is the Avogadro number, $\rho$ is the density of copper and $A$ is its atomic weight. Knowing $\lambda$, you can calculate the relaxation time as
Substitute all these results in the first expression and you are done.
- This is an experimental way of doing the job. Standard values are available on textbooks and internet.
- Caution: Use a very long copper wire (10 m or above) or use mV range potential. The current density of copper is very large.