Drift velocity

We must have seen car moving on the road.

To know how fast a car is moving we should know the velocity of a car.

Similarly, to know that how fast an electron is moving we have to know it's drift velocity.

Let us know about drift velocity.

When an electric field $\vec{E}$ is applied across the ends of the conductor

The free electrons experience a force in a direction opposite to that of the applied electric field.

The accelerated electrons collide inelastically with the ions in the conductor.

While moving, electrons continuously collide with positive ions.

These collisions cause electrons to change their direction of motion.

The two-process of collision and acceleration makes the electrons to move in a direction opposite that of the applied electric field.

When these electrons are moving, they acquire average velocity, that velocity is known as drift velocity.

Electrons cover some distance between two successive collisions.

Average distance travelled by free electrons between successive collisions is mean free path.

Electrons collide at random intervals and not regularly

Average time between successive collision of all free electron is called relaxation time.

Electrons move randomly in the absence of electric field

Random movement of all free electrons results in zero average displacement.

Zero average displacement results in zero average velocity.

But in presence of electric field, free electron experience force

The magnitude of Force experienced by an electron in the presence of the electric field is as above.

Force is given as the product of mass and acceleration. So the acceleration of electron is as above.

The negative sign shows the electron is accelerated in a direction opposite to electric field.

There is an average displacement of all free electrons due to this acceleration.

As there is acceleration, electrons must have some average velocity.

Average velocity of electrons in presence of electric field is called drift velocity.

To calculate drift velocity, let us apply electric field at time t=0.

Since electric field is just applied, initial velocity, u = 0.

Then electrons travel with average velocity $v_d$ for time $t$.

Using kinematical equation of motion.

Applying it here, we get

Drift velocity is given as above.

We can notice that the direction of drift velocity $V_d$ is opposite to the direction of E.

Let’s try to relate drift velocity to current.

Consider conductor with cross-section area A and electric field E.

Let electrons cover $\Delta x$ distance with $V_d$ velocity in $\Delta t$ time.

We know that charge variation is given by,

Multiply and divide R.H.S. by volume $V$.

Putting value of $N$ we gets,

The volume traveled by electrons in given time ,

Putting value of $V$ ,

Now on rearranging we get ,

Rearranging to make L.H.S. like expression of current,

Since, Charge flowing per unit time is current,

Hence, current is directly proportional to drift velocity.

Revision

Average distance travelled by free electrons between two successive collisions is called its mean free path.

Average time between successive collision is called relaxation time.

Average velocity of electrons in presence of electric field is called drift velocity. It is denoted by $V_d$.

Current and drift velocity can be related as,

The End