Difference Between Drift Velocity and Mobility

The average velocity can be thought of as drift velocity. In drift velocity, a phenomenon observed pertains to drifting of electrons in the presence of an electric field. It contributes to the electric current when used (or drift speed). Collisions with metal ions are caused by random motion produced by thermal velocity.

Subatomic particles like electrons are always moving in any direction. While moving slowly in the direction of the applied electric field, electrons do move randomly when subjected to an electric field. The aggregate speed of these electrons is referred to as the drift velocity.

Drift velocity is characterised by:

• The typical speed that charged particles, like electrons, travel at in a material when exposed to an electric field.

• M/s is the SI unit for drift velocity. Additionally, it is expressed in m2/(V.s)

Mobility of an Electron: 

The drift velocity of an electron for a unit electric field can be used to define an electron's mobility. The magnitude of the drift velocity created per unit strength of the electric field applied across the conductor is used to characterise the mobility of  a free electron or an ion, or a hole. Mobility (u) is therefore equal to vd/E, where vd is the drift velocity and E is the intensity of the electric field. m2/volt second is the SI unit for mobility.

Relationship Between Drift Velocity and Current Density:

The total amount of current flowing through a unit cross-sectional conductor in a given amount of time is known as the current density. The drift velocity formula looks like this:

$I = nAvq$

$J = I/A$  or, $J = nvq$

Where, J is the current density

I is the current 

A denotes the area of cross section

q is the charge

v is drift velocity of electrons

Derivation for the Expression of Drift Velocity: 

If a conductor of length l has a potential difference V formed at its ends, then $E=V/l$ is the formula for the electric field's intensity. Each free electron of magnitude $F=eE$, where e is the charge on an electron, experiences the electric force F. The electron's acceleration 'a' is equal to the force F/m, where m is the electron's mass.

$a = \left ( eV/l \right )/mv$

⟹ $a = eV/ml$………………………..(1)

It will move in the opposite direction of E, or in the direction of F.

Drift velocity is defined as$V_{d} = \left [ \left (u_{1}+at_{1}  \right )+\left (u_{2}+at_{2}  \right )+\left (u_{3}+at_{3}  \right )+...+\left (u_{n}+at_{n}  \right ) \right ]/n$

, where u1, u2... are electron velocities and t1, t2... are times.

$V_{d}= a\left ( t_{1}+t{2}+...+t_{n} \right )/n + \left (u_{1} + u_{2} +......+u_{n} \right )/n$

Since the average thermal velocity in the absence of an electric field is 0, $\left (u_{1}+u_{2}+......+u_{n}\right )/n$ equals 0.

$V_{d}= at = \left ( eV/ml \right )t$, where t is the relaxation period, follows as a result for the expression of drift velocity.

Derivation for the Expression of Mobility: 

In our knowledge, $V_{d}= \left ( eV/ml\right )t$. Any charge carrier with mass m and charge q has a drift velocity that may be calculated using the formula  $\left ( qV/ml\right )t$. When we enter the value of vd into the Mobility formula, we get the result $\mu=(\left (Vq/ml  \right )t)/E$, where t is the charge carrier's relaxation time, V is the potential difference between conductors, and l is the conductor's length.

$\mu = \left (qV/ml  \right )/E$

$qt/m = \left (q.E.l.t\right )/mlE$.

We are aware that for an electron, $q = e$, where e is the electron's charge.

Mobility is therefore equal to $\mu= e.t/m$, where m is the electron's mass.

Differentiate Between Drift Velocity and mobility: 

Summary

It is crucial to differentiate between drift velocity and mobility because these are two key ideas in the chapter on current electricity. The average speed that electrons gain when moving through an electric field is what is known as drift velocity. The average velocity is taken into account since charged particle travel is not in a straight line due to particle collisions. The definition of mobility is "drift velocity per unit electric field." It may be said that the mobility is based on the types of solids and that the larger the mobility, the faster the movement of particles in a given field strength.