Average time since last collision:
Average time between collisions:
Avg. drift velocity:
This app illustrates the Drude model of conduction in metals. The window shows a piece of a wire that one should imagine extends vertically above and below the window. The red dots are lattice atoms in the wire and the red bars are its edges. The blue dots are Newtonian electrons, which have random thermal motions, and bounce elastically off the lattice atoms and each other. The dashed yellow bar "rides" with the electrons' average vertical velocity component. Using the controls at the right, one can vary the field strength and the thermal speed of the electrons, and one can fix the wire's effective temperature by removing electrons' kinetic energy at the same rate as the electric field supplies it. The app calculates the average time since the last collision and the average time between collisions by taking a straightforward average of these quantities over all electrons.
One can set the temperature to "normal," "very hot," or "very cold." The root-mean-square electron speed in the "very hot" setting is twice that in the "normal" setting, meaning that the absolute temperature is four times higher. The "very cold" setting has an absolute temperature 64 times colder than "normal," to make the electron speed slow enough so that you can see how the computer handles collisions and see the electrons moving in ballistic trajectories in response to the field. But the electron speeds in this model are all unrealistically slow: at room temperature, the average thermal electron speed in a newtonian model (as you can verify) would be approximately 20 trillion (10^12) atom-widths per second.
Though the app unrealistically executes newtonian collisions at unrealistically low temperatures, one can still use it to demonstrate theoretical implications of the Drude model, such as that the average time since the last collision with a lattice atom is the same as average time between such collisions, that the average drift speed is proportional to the field strength, and that increasing the temperature reduces the drift speed. Note that when the the temperature is fixed or the field is zero, the displayed drift velocity (which is the average vertical component of the electrons' velocity) is a running average since the last change in conditions, but it can still take several minutes to settle down to a relatively stable value. When the field is nonzero and the temperature is not fixed, the drift velocity is averaged over only one second.