Thorough Understanding of Drift Velocity and Mobility

When a potential difference is applied across the ends of the conductor, the electric field is generated within the conductor and the free electrons experience force in the opposite direction of the applied electric field. The potential difference applied does not accelerate the electrons but provides a constant velocity in the direction contrary to the electric field generated within the conductor. This small constant velocity is drift velocity. The progression of electric current through materials is caused by the Mobility of charge carriers inside the materials. The free electrons are the charge carriers in the metallic conductors. The students need to distinguish between drift velocity and Mobility.

What is the definition of drift velocity?

Drift velocity can be considered as the average velocity. In drift velocity, electrons ‘drift’ in the existence of an electric field. It is used to (or drift speed) contributes to the electric current. Indifference, thermal velocity generates random motion, which results in collisions with metal ions.

What is the definition of the mobility of an electron?

The mobility of an electron can be defined as the drift velocity of an electron for a unit electric field. 

State the relation Between Drift Velocity and Current Density

The current density can be defined as the whole amount of current flowing via a unit cross-sectional conductor in unit time. The formula of drift velocity can be written as:-

I = nAvQ

J = I/A = nvQ

Where,

• J stands for the current density and it is measured in Amperes per square metre

• v stands for the drift velocity of the electrons

• A is cross-section area of conductor

• Q stands for the charge

Definition and expression of drift velocity

The drift velocity is defined as the net velocity acquired by the free electrons under the influence of the electric field developed within the conductor by the potential difference, which is applied across the ends of the conductors.

Suppose a potential difference V is established across the ends of conductor of length l, then the magnitude of electric field intensity E is given by E=V/l. The electric force F is experienced by each free electron of magnitude, F=eE, where e is the charge on an electron. The magnitude of acceleration ‘a’ produced in the electron, a=F/m, where m is the mass of the electron.

a = (eV/l)/mv 

⟹ a = eV/ml………………………..(1)

It will be in the direction of F, i.e. in the opposite direction of E.

Drift velocity, Vd={(u1+at1)+(u2+at2)+(u3+at3)+……..+(un+atn)}/n, where u1, u2…are the velocities of electrons and t1, t2…are the times.

⟹Vd = (u1 + u2 +……+un)/n + a(t1+t2+…+tn)/n

Here, (u1+u2+……+un)/n = 0 since the average thermal velocity in the absence of an electric field is 0.

Therefore, Vd = at = (eV/ml)t where t is the relaxation time.

Definition and expression for Mobility.

The Mobility of a charge carrier like free electron, ions and holes is defined as the magnitude of the drift velocity developed per unit strength of the electric field applied across the conductor. Therefore, mobility (u) = vd/E, where Vd is the drift velocity and E is the electric field intensity. The SI unit of Mobility is m² /volt second.

We know that vd=(eV/ml)t. The magnitude of the drift velocity of any charge carrier having mass m and charge q is given by (qV/ml)t. Putting the value of vd in the Mobility formula, we get μ=((Vq/ml)t)/E, where t is the relaxation time of the charge carrier, V is the potential difference across conductors, and l is the length of the conductor.

 μ= (qV/ml)/E 

⟹ μ=(q.E.l.t)/mlE = qt/m.

We know that for an electron, q = e, where e = charge of the electron.

Therefore, mobility, μ= e.t/m, where m is the mass of the electron.

Drift velocity vs Mobility

Now, let’s distinguish between Mobility and drift velocity. Drift velocity is the small velocity acquired by the electrons when a potential difference is applied and an electric field is produced. Its SI unit is m/s.

On the other hand, the Mobility of an electron is the magnitude of the drift velocity per unit of the electric field. Its SI unit is m² /volt second. Mobility of the material depends upon the charge carriers. In conductors, charge carriers are free electrons, ions are charge carriers in electrolytes and semiconductors like germanium and silicon have holes and electrons as charge carriers.

Mobility, μ = Vd/E, where Vd is the drift velocity and E is the electric field intensity. The drift velocity and mobility formula are also way different.

Conclusion 

Drift velocity and Mobility are important concepts in the current electricity chapter and it becomes necessary to distinguish between drift velocity and Mobility. Drift velocity is nothing but the average velocity acquired by the electrons under the influence of an electric field. The average velocity is considered since the motion of charged particles is not in a straight line due to the collision with other particles. Mobility is defined as drift velocity per unit electric field. It can be concluded that larger the Mobility, faster the movement of particles in a given field strength and Mobility is dependent on the types of solid.