# Drift Velocity of Electron

## Drift Velocity of Electron

To understand drift velocity, assume that there is a conductor.

And, there are *n* number of free electrons per *m ^{3}* of the conductor.

Let us assume that the axial drift velocity of these electrons be *v* meters/second.

See the figure below to understand the situation.

Now, we all know that *Distance = Speed x Time* .

Hence, In time *dt*, distance travelled by these electrons would be would be *v x dt* .

Now, let us assume *A* to be the area of cross-section of this conductor.

Then the volume would be *vAdt*

And the number of electrons contained in this volume would be *nvAdt.*

Obviously, all these electrons will cross the conductor cross-section in time *dt.*

If *e *is the charge of each electron, then total charge which crosses the section in time *dt* is *dq=nAevdt.*

Since current is the rate of flow of charge, it is given as

*i = dq/dt*

*or, *

*i = nAev dt / dt*

*or,*

*i = nAev*

Now, we know that Current density, *J =i/A = nevA* ampere/metre^{2}

Assuming a normal current density J = 1.55 x 10^{6} A/m^{2}, n=10^{29} for a copper conductor and e = 1.6 x 10^{29} coulomb, we get the drift velocity to be about 0.58 cm/min. Thus we see that the electron drift velocity is very slow.

Now let us test our understanding of electron drift velocity with the help of an example.

**Question :** A conductor material has a free-electron density of 10^{24} electrons per metre^{3}. When a voltage is applied, a constant drift velocity of 1.5×10^{-2} metre/second is attained by the electrons. If the cross-sectional area of the material is 1 cm^{2}, calculate the magnitude of the current. Electronic charge is 1.6 x 10^{-19} coulomb.

**Answer :** The magnitude of the current is

** i = nAev**

Where,

n =10^{24}

A= 1 cm^{2} = 10^{-4} m^{2}

e = 1.6 x 10^{-19} C

v = 1.5 x 10^{-2} m/s

Substituting these values, we get :

i = 10^{24} x 10^{-4} x 1.6 x 10^{-19} x 1.5 x 10^{-2}

or,

**i = 0.24 A**

Now, we understand the drift velocity of electron. However, there are two more things that we need to understand:

- Velocity of charge
- Velocity of propagation of electric field

**Velocity of charge** is the speed with which charge drifts in a conductor. It’s value is very low (fraction of a metre per second).

**Velocity of propagation of electric field**, is the speed with which the effect of e.m.f. is experienced at all parts of the conductor resulting in the flow of current. Its value is very high (3×10^{8} m/s).