Dimensions of Mobility

Dimensions of Mobility: There have been a lot of free charges for good conductors. Metals that are free of charge are referred to as having free electrons. The travel distance between an electron that can move collisions with atoms and other electrons is very small. As a result, the electron pathways appear at random, similar to the movement of atoms in a gas. Even so, an electric field exists in the conductor, causing the electrons to drift straight at the indicated angle (opposite field, as negative).

Whenever it comes to mobility, it can be defined as the drift velocity per unit of electric field strength. By evaluating the definition, we can conclude that the greater the mobility, the faster the particles move at the applied electric field strength. This should be noted that the mobility of a specific particle in a solid varies with temperature.

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Characteristics of Mobility

The mobility of distinct solid materials varies because the motion of each solid is not always caused by electrons (negatively charged particles). Using semiconductors as an example, we can say that the electric current or charge flow in them is also carried by the motion or movement of the positively charged holes. Such charged holes correspond to the absence of an electron, influencing the overall determination of hole mobility and electron mobility separately.

The temperature has an effect on solid and liquid matter mobility because it increases the movement of the atoms and particles that make up the solid or liquid. As a result, there are more collisions and the mobility is altered.

Dimensional Formula of Mobility

The dimensional formula of Mobility can be represented as:

[M^-1 L⁰ T² I¹]

Here,

M = Mass

L = Length

I = Current

T = Time

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Derivation

As we know, Drift velocity = Mobility × Electric Field

Then, Mobility (M) = Drift velocity × [Electric Field]^-1 . . . . (1)

So, the dimensional formula of drift velocity = [M⁰ L¹ T^-1] . . . . . (2)

It is known that, Electric Field = [Force × Charge^-1]

Now, the dimensions of force and charge = [M¹ L¹ T^-2] and [I¹ T¹] respectively.

Thus, the dimensional formula of Electric Field = [M¹ L¹ T^-2] × [I¹ T¹]^-1 = [M¹ L¹ T^-3 I^-1] . . . (3)

When substituting equation (2) and (3) in equation (1) we get,

Mobility = Drift velocity × [Electric Field]^-1 or M = [M⁰ L¹ T^-1] × [M¹ L¹ T^-3 I^-1]^-1 = [M^-1 L⁰ T² I¹].

Thus, mobility has been dimensionally represented as [M^-1 L⁰ T² I¹].

Also Read: Dimensions Of Work

FAQs

What actually occurs if no current flows through a conductor?

As if no current is passed through a conductor, that is, when the conductor's electric fields are inactive or are not applied to the conductor, electrons are moved along a straight path at constant speeds and collide with lattice ions (positive). With each collision, the direction of electrons is changed at random. As a result, the resulting path of an electron is a random sequence of straight segments over a long period of time.

Is mobility a scalar quantity?

The drift velocity per unit electric field has been defined as mobility. As a result, it is a scalar quantity.