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:

• Dimensions of Pressure
• Dimensions of Weight
• Dimensions of Power of Lens
• Dimensions of Universal Gas Constant
• Dimensions of Gravitational Potential Energy