Dimensions of Permittivity

Dimensional Formula of Permittivity (Free Space or Vacuum)

The dimensional formula of Permittivity of free space or vacuum is given by,

M-1 L-3 T4 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 = [M-1 L-3 T4 I2]

Therefore, the permittivity of free space or vacuum is dimensionally represented as M-1 L-3 T4 I2.

⇒ Check Other Dimensional Formulas:

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