# How far do electrons actually move along a conductor under an alternating current?

This is more or less a curiosity question. But I have had really good luck with stack exchange so far. If I can expand on my question a little bit - it may not be super important, but I know under say a typical household circuit, under alternating current, all wires are under either 120v or 240v single phase power at 60 htz. Each htz being one cycle going from (I believe) 0v to +120 v back to 0v to -120v and back 0v. My query is basically, between say our start at 0v and the first crest at +120v, and we'll say for simplicity this is occurring on a standard household 12 AWG size wire, how far do the electrons manage to move along the conductor? is it just a few inches? is it a couple feet? fractions of an inch? Would this change substantially if it were 240v single phase or say the 480v phase voltage you'd get between phases of a wye transformer?

Final note: I am not the best with most scientific equations. Some simple ones maybe but if your answer is in the form of like a set of logarithmic equations it would be appreciated if you could maybe "dumb down" the answer for me :)

EDIT: David White - So given that during a single hertz, or cycle, we have electrical pressure going in one "direction" for half that cycle and then pressure going in the other direction for the second half of that cycle, so I can think of it now as pressure (which I understand varies, as we move from 0 to +120 crest and back to 0) going in one direction for 1/120 of a second and an APPROXIMATE (using your calculator to establish 5 amps across a 12 guage/2.05mm conductor) drift velocity of 40cm/hr or (0.1 mm/s) so then it would then be 0.1mm x 1/120th = "the electrons" "move" about .0008 mm along this given conductor? Is that accurate at all? I apologize if I am oversimplifying this.

• This relates to a question I've had. Books show AC current in the same direction as voltage gradient. I posted about whether there is inertia to the electrons so that immediately after the shift from forward to reverse voltage, does the current proceed in the forward direction (now against the gradient) for a bit more time until the kinetic energy is depleted, and only then will the electrons then resume down their electrostatic gradient in the reverse direction? physics.stackexchange.com/questions/404937/… – lamplamp Jan 23 '19 at 21:25
• @lamplamp In a circuit, this "inertia" of a current to change would be termed "inductance". – BowlOfRed Jan 23 '19 at 21:30
• ElectricianPat, you are correct. In the situation of A/C current, the electrons "wiggle" rapidly about fixed positions, but they don't "flow" through the wire. – David White Jun 2 at 17:27

Conduction electrons move at very high speeds of millions of meters per second. These speeds cancel out in the absence of a field. When an electric field is applied electron drift results with a very small velocity $$v=\mu E$$. $$\mu$$ is the mobility. Typical values are of the order of micrometers per second. To calculate the distance traveled due to an alternating field you need to specify $$E = V/l$$ where $$l$$ is the length of the conductor. Note that alternating voltages are given in rms values and that the peak value is $$\sqrt{2}$$ times higher. Finally the maximum displacement is $$d_{max} = \frac{1}{2\pi f}\sqrt{2}\mu V/l$$. $$f=50 Hz$$. For Cu the mobility is about 6 $$10^{7}$$ Siemens/m.