Dimensional Formula of Mobility

Mobility is defined as the value of per unit drift velocity in relation to electric-field strength. As an introduction to mobility, it can be said that mobility regarding a specific particle is in solid form, and it also can be varied due to different temperatures.

Understanding Mobility of an Electron

Let Vd is the drift velocity and E is the electric field applied to the conductor, then mobility ‘μ’ is represented as:

Mobility = Drift velocity * Electric field

μ=VdE

Factors Affecting Drift Velocity:

The main factors on which the drift velocity is dependent are:

•     Temperature: With an increase in temperature, atoms of the material start vibrating at a fast speed. Hence, the associated movement of the electrons increases. Thus, drift velocity increases with an increase in the temperature of the conductor.
•     Potential difference: The potential difference applied across the cross-section of the conductors increases the current flowing through it. This increase in current causes the electrons to vibrate quickly. Thus, with an increase in potential difference, the drift velocity of the electrons increases.
•     Area: The more area required to be covered by the electrons decreases their energy. Electrons prefer to pass through the shortest distance, which significantly increases with an increase in the cross-sectional area of the conductor. Hence, with an increase in the cross-sectional area of the conductor, the drift velocity of the conductor decreases. Thus, the area of the conductor and its drift velocity are inversely proportional to each other.

The formula for calculating drift velocity is as follows:

Let ‘I’ is the charge passing through a conductive material in amperes,

‘n’ is the total number of charged particles or electrons,

‘A’ is the cross-sectional area of the material,

‘vd’ is the drift velocity of charged particles in the material, and

‘Q’ is the electron charge in Coulombs.

Then,

I=nAvdQ

Dimensional Formula of Mobility

The dimensional formula of mobility has defined an expression regarding physical terms. The base of the dimensional formula of mobility has an appropriate and proportionate relation with proper dimensions. For instance, dimensional force is F= [MLT-2]. It has been observed from the studies that to measure the dimensional formula of mobility, the dimension formula of drift velocity needs to be divided by the dimensional formula of the electric field. Mobility is mainly a measurement of the speed of electrons that pass through conductors. Therefore, the dimensional formula of mobility is [M1 L2 T-4I1]

Derivation of Dimensional Formula of Mobility

Mobility = Drift velocity * Electric field

The dimensional formula of drift velocity will be the same as velocity. 

So, it is equal to = [M0 L1 T-1]

Electric field = ForceCharge

Dimensional Formula of Force = [M1 L1 T-2]  and 

Dimensional Formula of Charge = [M0 Lo I1 T1]

Dimensional Formula of Electric field = [M1 L1 T-2] [M0 Lo I1 T1]

Dimensional Formula of Electric field  =  [M1 L1 T-3I1]

Dimensional Formula of Mobility =  Drift velocity * Electric field

Dimensional Formula of Mobility= [M0 L1 T-1]  *  [M1 L1 T-3I1]

Dimensional Formula of Mobility= [M1 L2 T-4I1]

Conclusion

Thus, it can be concluded that mobility is mainly the value of the per-unit drift and also the measurement of the electron in a conductor. This article provided a quick understanding of the basics of drift velocity, a quick formula to calculate drift velocity, and the mobility of the electrons. It is the average velocity of the charged particles or electrons. The established relation between this velocity and electric current helps further relate it to the current density.