[chris]

I thought it would be a good academic exercise for us to do the calculation:

Let's imaging a notional conductor, a cylindrical piece of wire.

Its cross-sectional area is A, the length is d and there are n charge carriers, e, moving at velocity v.

Therefore the total mobile charge, Q, in the cable is given by Adne

Time, t, for this charge to move along the conductor = d/v

Since current, I, = Q/t we can substitute for the above:

I = Adne / d/v = Avne

So v = I / Ane

Now i need some numbers for my notional copper wire including - number of charge carriers etc...

Who would like to take up the baton...

[jeffreyH]

Or you could read this.

http://resources.schoolscience.co.uk/CDA/16plus/copelech2pg3.html

[vhfpmr]

The drift speed of an individual electron in a current-carrying copper wire is about equivalent to fast walking pace.

Not by a very long chalk, the drift velocity of a 1A current in a 2mm copper wire is 23 microns per second.

//en.wikipedia.org/wiki/Drift_velocity

[chris]

Thank you; can we please complete my calculation above to show how we know this?

[vhfpmr]

The calculation is on the wiki page above.
n =8.5E28
e =1.6E-19

[jeffreyH]

I thought it would be a good academic exercise for us to do the calculation:

Let's imaging a notional conductor, a cylindrical piece of wire.

Its cross-sectional area is A, the length is d and there are n charge carriers, e, moving at velocity v.

Therefore the total mobile charge, Q, in the cable is given by Adne

Time, t, for this charge to move along the conductor = d/v

Since current, I, = Q/t we can substitute for the above:

I = Adne / d/v = Avne

So v = I / Ane

Now i need some numbers for my notional copper wire including - number of charge carriers etc...

Who would like to take up the baton...

So if we take the cross sectional area A = 0.003m, velocity v = 1 m/s, number of charge carriers n (in copper) = 8.5 x 10²⁸ per m³. Then we need d to derive the volume of the wire to proceed. If we just assume it is 1 cubic metre anyway this simplifies things. Electron charge is 1.6 x 10^-19C. So now we have the figures to calculate current and subsequently drift velocity. Then all we need do is change the value for current to see how this affects drift velocity. We could even calculate a hypothetical current needed to bring drift velocity close to c, just for fun.

[jeffreyH]

For v = 1 m/s you appear to get 40.8 million amps. This may be wrong! Very likely so.

[chris]

Whoops!

[lightarrow]

I know that if we switch on a torch on a train, the speed of light cannot be added to that of the train. What about speed of electricity on a wire? Can it be added to the train's speed?

It depends on
1) what you intend with "speed" (speed of what?)
2) what you intend with "electricity"

Just to make an example, the phase velocity of electromagnetic waves in a wave-guide can be greater than c. Even the group velocity of an electromagnetic wave, in a suitable medium, can be faster than c.
What instead must always be less then or equal c is signal velocity
http://www.mathpages.com/home/kmath210/kmath210.htm