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Dimensions of Mobility

Last updated date: 13th Jul 2024
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What is Drift Velocity?

There are a large number of free charges on good conductors. Metals, free of charge are termed free electrons. The distance of the travel is very small between an electron that can move collisions with atoms and other electrons. Thus the electron pathways appear randomly, such as the movement of atoms in a gas. However, there is an electric field in the conductor that causes the electrons to drift straight at the indicated (opposite field, as negative). 

Drift velocity is a free-charged estimate after field application. Drift velocity is very low, as there are many free charges. Given the ratio of free electrons to a conductor (the number of electrons per volume of a unit), it is possible to calculate the flow rate of a given current. When there is large congestion, it reduces the required speed to a given stream.

Electron Mobility & Drift Velocity

Quantum mechanics tells us that electrons represent random movements. When the switch is turned on to light our lamp, an electric field is created near the cord that attracts the electron to the high power, which is the positive side of the battery. When the electrons go to the positive, they jump on the atoms in the wire. 

The combination of their random internal movements and their collision with atoms causes electrons to move and giggle in their movement. In this drawing, the black dots are the copper atoms, and the tiny red dots represent the electron as it jumps between atoms. The road is disabled, but net removal is on the right.

Electron mobility is the way an electron can move faster in a conductor. Determination of flood speed and power field.

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].


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 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 with in 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.

FAQs on Dimensions of Mobility

1. Explain the term 'drift velocity of electrons in a conductor. Also, obtain the expression for the current by a conductor in relation to 'drift velocity?

The drift velocity is defined as the free electrons of the conductor which is counted to be the average velocity of all the free electrons inside the conductor. Whenever a conductor remains connected to a source of emf the electricity is established inside the conductor. Therefore, the formula of drift velocity in an electric field conductor is the ratio of V and L, where V belongs to the potential difference across the conductor and L is equal to the length of the conductor. There are opposite directions for both acceleration and electric field where the electrons attain a velocity in addition to thermal velocity in the direction opposite to that of the electric field.

2. What is the relaxation time of electrons according to drift velocity?

The difference between the average time of two consecutive collisions is known as the relaxation time of electrons. The drift velocity expression reveals that the relaxation time is the interval of time between the successive collisions of an electron when a temperature increases, the electrons move faster and thus more collisions occur quickly. This is the reason why relaxation of time decreases with an increase in temperature. This implies that drift velocity is also decreased with a decrease in temperature.

3. What happens when no current is passed through a conductor?

When no current is passed through a conductor, that is when the electric fields of a conductor are inactive or not applied to the conductor, then electrons are moved along the straight path which is at constant speeds and collide with the lattice ions (positive). The direction of electrons is changed randomly with each collision. Hence, the resulting path of any electron covers many collisions which is a random sequence of straight segments over a long period of time.

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