# Charge displacement through a conductor

I read this in book that if we consider a conductor in which current I is flowing at a potential difference of V then in time ∆t charge equal to I ∆t will flow across the ends of conductor. But in time ∆t that much amount of charge will only be able to travel distance equal to drift velocity multiplied by the time i.e.Vb x ∆t, isn’t it.
Please tell me how this happens.

## Answers and Replies

That's how it happens. There are a lot of electrons so the drift speed is low. (the first v is voltage, vb is velocity. You probably knew that.)

Thanks Antiphon for responding.
But I want to know that if a current I is flowing in a conductor it would mean that in one second charge equal to magnitute of I would be able to flow across a area placed perpendicular to the flow of current but if we take 'centre of charge' in to consideration it would mean that much amout of charge has displaced through a distance equal to drift velocity , then how we can say that ,that much amount of charge has traversed a distance equal to the lenght of conductor i.e. across its ends ?

K^2
Science Advisor
Imagine a particle placed in a pipe every meter. The particles travel at 1m/s. How many particles flow through a specific location in the pipe every second? One. What if you had 2 particles per meter? Then two, right?

Well, there are about 3x10^23 electrons for every gram of conductor. That's about 50,000 coulombs of charge. Granted, not all of these participate in conduction, but even if it's just 1 in 29, like in copper, the electrons would generate a significant current just barely moving.

It's easy enough to compute the velocity given a current and the wire gauge. Again, lets consider copper.

8.94g/cm³
Z=29
63.55amu
1 valence electron.

Consider 22 gauge wire = 0.64mm. That's cross-section area of 3.2x10-7m². That's 2.86g of copper per meter of wire. That's 2.73x1022 conduction electrons. That's 4,370 Coulombs.

At 1 Amp, only 1/4370th of electrons in 1m of wire have to move through to give you 1 Coulomb per second. That's 0.23mm/s. If you could see the electrons, you'd have to look very carefully to notice they are moving at all at these speeds.

tiny-tim
Science Advisor
Homework Helper
Welcome to PF!

Hi gemma786! Welcome to PF! I'll just add this to what K^2 has said …

to put it into persepective, the drift speed is also very much smaller than the random speed of the electrons (or rather, of that very small proportion of electrons which have escaped from the Fermi sea of lowest-energy-states electrons) …

http://en.wikipedia.org/wiki/Electron_mobility#Conceptual_overview"
… typical drift speeds in copper being of the order of 10-4 m·s−1 compared to the speed of random electron motion of 105 m·s−1

Last edited by a moderator:
Thanks to both of you.
But I am thinking about it as follows :-
I am speculating that for a bit let us consider the rate of charge flow through a conductor as charge separation taking place in giving time then charge separation which takes place in time dt will be IxdtxVbxdt for a current I flowing through the conducor and throughout the conductor this charge separation will be (NxIxdt)xVbxdt <N=length of the conductor (l)/ drift velocity X dt> where (NxIxdt) stands for total charge displaced through distance Vbxdt. By putting value of N if above relation it comes that total charge separation through the conductor is Ixdtxl.In other words in time dt charge equal to Ixdt has travelled across the length of the conductor.
I don't know ! it is just mere speculation or it has some generality.
If you don't mind I would like like to listen to your comments over it .
Thank you very much.

as charge separation

never heard of such a thing..can you describe?? Conduction electrons just bounce along from atom to atom..never heard about any material change in distances between electrons. In fact post #4 appears to refute that very idea.

think of water molecules flowing down a river...their separation plays no part in the measurement of water flow....

K2: great post #4....KUDO'S...about the best description of current flow I have seen....

Naty1 you gave a very right complement about K2.
As far as that idea is conserned consider a momentary flow of charge on the application of definite electric field as long as that charge separation generates its own electric field to counter attack the external electric field and think about the potential of negative charge that decreases in going from a region of higher potential to lower potential.