# Current is flow of charge with constant velocity; Why not accelerated?

1. Oct 19, 2011

### vkash

When a potential difference is applied across a conductor. then a electric field is formed across it. There are free electrons in conductor which should accelerate because of there is electric field. Since all we know that Force =charge*Electric_field.
But it is not so. Inside a conductor electrons even not able to reach speed of a meter per second. Why it is so?Why not they accelerate?
When this thought come in my mind, firstly i think that there is inelastic collision between the electrons that causes heating of conductors and maintains constant speed of electrons. But collisions between the electrons is elastic and elastic collisions doesn't convert mechanical energy to heat. So finally we can say Center of mass of all the electrons should accelerate but they move with constant speed.
that's all i want to say.

Last edited: Oct 19, 2011
2. Oct 19, 2011

### sophiecentaur

What about the mean square velocity of these little devils you talk of?

3. Oct 19, 2011

### vkash

Does not understand:grumpy:

4. Oct 19, 2011

### sophiecentaur

Electrons don't just sit there, waiting to be pushed along by an electric field. They are in constant motion, randomly, in all directions with a range of speeds, up to many km/second, depending on the temperature. They behave like a gas.
When a Potential Difference is applied over a length of wire, this huge number of electrons will gain a very small net velocity along the wire (the drift velocity).
For a very short time, after the PD is applied, there will be an initial acceleration until the drift velocity is reached but they will not just get faster and faster on their journey along the wire. The extra kinetic energy of the electrons will be dissipated in passing through the metal lattice- they will not accelerate.
This is different from Electrons in a vacuum, which will accelerate as they are pulled by an electric field. Their final Kinetic Energy being equal to the Potential Difference across which they have been accelerated.

5. Oct 19, 2011

### nasu

You are in principle right in saying that collisions of the electrons (or scattering) dissipates the energy gained in the electric field. However the main factor is scattering on the lattice vibrations and impurities and not electron-electron scattering.
In the simplest model, the resultant drift velocity depends roughly on how much the electrons can be accelerated between two collision (on average).

6. Oct 20, 2011

### vkash

Thanks to both persons. It's something inside the lattices of resistances.

Last edited: Oct 20, 2011
7. Oct 20, 2011

### sophiecentaur

When there is no applied pd the electrons and the lattice will be in thermal equilibrium. An equal amount of energy will go each way. Any net velocity change in the electrons due to an applied E field will go to zero after an 'impact' with the lattice. I'm just trying to square what momentum conservation does here. Where does it 'go'?

8. Oct 20, 2011

### nasu

The conservation of momentum for the inelastic scattering of electrons on lattice includes creation (or annihilation) of lattice oscillations (or phonons according to the usual picture).
It may also include a term that may be associated with the recoil of the lattice as a whole for the so-called "umklap" scattering (which may be the major contribution to electric resistivity).
The resistivity is due to the vibrations of the lattice and not the lattice itself.