Dimensions of Mobility

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Introduction

In physics, the term mobility has a broad meaning. When we consider the state of solid and liquid, the mobility of the electrons determines how fast an electron can move through a metal or any semiconductor when an electric field is applied. These particles are either pulled by the electric field or collide with the atoms of the solid. When the electrons are pulled along the electric field and time to time collide with atoms or each other, this combination results in the particle to move with an average velocity, termed as drift velocity. 

The particle referred to here is a negatively charged electron, in metals.

Definition of Mobility

When we have to define mobility, it can be defined as the value of the drift velocity per unit of electric field strength. By analyzing the definition we can conclude that the faster the particles move at applied electric field strength, the larger the mobility. It is to be noted that the mobility of a specific particle in the solid may vary at different temperatures. 

Dimensional Formula of Mobility:

Mobility: Vd / E, is the Dimensional Formula of Mobility.

 Where, Vd = Drift Velocity and E = Electric Field applied.

Characteristics of Mobility

Mobility varies for different solid materials because in every solid the motion is not necessarily caused by the electrons (negatively charged particles). Taking the example of the semiconductors, we can say that the electric current or flow of charge in them is also carried by the motion or movement of the positively charged holes. These charged holes correspond to the absence of an electron, thereby, affecting the entire determination of hole mobility and electron mobility separately. 

The temperature affects the mobility in the solid and liquid matter because it lands up increasing the movement of the atoms and particles building up the solid or liquid. This results in frequent collisions and in causing an alteration in the mobility. 

Dimensions of Mobility

Speaking of dimension, it is a mathematical space, which is defined as the minimum number of coordinates required to specify any point within it. Every object has its own dimensions and it can be determined with the help of a mathematical expression. The dimension of mobility is as follows.

[M-1 L0T2I1].

Where, 

M= Mass, L= Length, I= Current, T= Time.

Derivations of Mobility Formula

[Drift Velocity can be explained as the average velocity which is attained by the charged particles, such as electrons, in a material due to an electric field.]

By the definition of Drift velocity, we know that Drift Velocity = Mobility x Electric Field.

So, we can say that Mobility = Drift Velocity/ Electric Field.

[Electric Field is the area around a charged particle or an object within which a force would be exerted on other charged particles or objects.]

By the definition of Electric Field, we know that Electric Field is a value of Force per unit Charge. i.e. Electric Field = [ Force/ Charge]

The dimension of Force is [M1L1T2] and the dimension of Current is [I1T1].

Therefore, we can obtain the dimension of the Electric Field by putting the dimension of force and charge in the formula of Electric Field. 

Electric Field = [M1L1T2] x [I1T1] = [M1L1T-3I-1]

Therefore by putting the values in the formula of Mobility, we can obtain the dimension of Mobility.

As we know, Mobility = Drift Velocity / Electric Field

The dimension of drift velocity is [M0L1T-1].

Mobility = [M0L1T-1] x [M1L1T-3I-1] = [M-1 L0T2I1].

Importance of Mobility

The importance of mobility is that it plays a vital role in electronic devices. The electronic devices require high mobility for them to function. For example, the batteries used in electronic appliances get charged with the help of electron mobility, and the semiconductors used in solar cells or electronic devices or transistors carry on their work due to mobility.