# Dimensions of Mobility

## Dimensional Formula of Mobility

The dimensional formula of Mobility is given by,

[M-1 L0 TI1]

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 [IT1] respectively.

∴ The dimensional formula of Electric Field =  [M1 L1 T-2] × [IT1]-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 TI1].

Therefore, mobility is dimensionally represented as [M-1 L0 TI1].