# 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 TI2

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Since, Force = [4πε]-1 × [Charge2] × [Distance]2

∴ Permittivity (ε) = [Charge2] × [Force]1 × [Distance]. . . . . (1)

⇒ Charge = current × time

∴ The dimensional formula of charge = [IT1] . . . . . (2)

The dimensional formula of distance = [M0 L1 T0] . . . . . (3)

⇒ Force = Mass × Acceleration

∴ The dimensional formula of force = [M1 LT-2] . . . . . (4)

On substituting equation (2), (3) and (4) in equation (1) we get,

Permittivity = [Charge]2 × [Force]1 × [Distance]2

Or, ε = [IT1]2 × [M1 LT-2]1 × [M0 L1 T0]2 = [M-1 L-3 TI2]

Therefore, the permittivity of free space or vacuum is dimensionally represented as M-1 L-3 TI2.

### ⇒ Check Other Dimensional Formulas:

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