Dimensional Formula of Mobility
The dimensional formula of Mobility is given by,
[M-1 L0 T2 I1]
- M = Mass
- L = Length
- I = Current
- T = Time
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].