Dimensional Formula of Permittivity (Free Space or Vacuum)
The dimensional formula of Permittivity of free space or vacuum is given by,
M1 L-3 T4Â I2
Where,
- M = Mass
- L = Length
- T = Time
Derivation
Since, Force = [4πε]-1 × [Charge2] × [Distance]–2
∴ Permittivity (ε) = [Charge2] × [Force]–1 × [Distance]–2 . . . . . (1)
⇒ Charge = current × time
∴ The dimensional formula of charge = [I1 T1] . . . . . (2)
The dimensional formula of distance = [M0 L1 T0] . . . . . (3)
⇒ Force = Mass × Acceleration
∴ The dimensional formula of force = [M1 L1 T-2] . . . . . (4)
On substituting equation (2), (3) and (4) in equation (1) we get,
Permittivity = [Charge]2 × [Force]–1 × [Distance]–2
Or, ε = [I1 T1]2 × [M1 L1 T-2]–1 × [M0 L1 T0]–2 = [M1 L-3 T4 I2]
Therefore, the permittivity of free space or vacuum is dimensionally represented as M1 L-3 T4Â I2.