Dimensions of Mobility

Dimensional Formula of Mobility

The dimensional formula of Mobility is given by,

[M^-1 L⁰ T² I¹]

Where,

• M = Mass
• L = Length
• I = Current
• T = Time

Derivation

Since, Drift velocity = Mobility × Electric Field

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

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

Since, Electric Field = [Force × Charge^-1]

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

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

On 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].

Therefore, mobility is dimensionally represented as [M^-1 L⁰ T² I¹].

⇒ Check Other Dimensional Formulas:

• Dimensions of Time Period
• Dimensions of Linear Density
• Dimensions of Velocity Gradient
• Dimensions of Boltzmann Constant
• Dimensions of Gravitational Potential Energy