Dimensional Formula of Dielectric Constant

The dimensional formula dielectric constant is given by,

[M⁰ L⁰ I⁰ T⁰]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Dielectric constant (K) = Permittivity of the substance (ε) × [permittivity of free space (ε₀)]^-1

Since, Force = [4πε]^-1 × [Electric Charge]² × [Distance]^–2

∴ Permittivity of substance = permittivity of free space = [Charge²] × [Force]^–1 × [Distance]^–2 . . . . . (1)

⇒ The dimensional formula of:

Charge = [I¹ T¹] . . . (2)

Distance = [M⁰ L¹ T⁰] . . . . . (3)

Force = [M¹ L¹ T^-2] . . . . . (4)

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

Permittivity (ε) or (ε₀) = [Charge]² × [Force]^–1 × [Distance]^–2

Or, ε = ε₀ = [I¹ T¹]² × [M¹ L¹ T^-2]^–1 × [L¹]^–2 = [M¹ L^-3 I² T⁴]

∴ the dimensions of permittivity of a substance or free space = [M¹ L^-3 I² T⁴]

Since, Dielectric constant (K) = ε × [ε₀]^-1

Therefore, the dielectric constant is dimensionally represented as [M⁰ L⁰ I⁰ T⁰] = Dimensionless Quantity

⇒ Check Other Dimensional Formulas:

• Dimensions of Dipole Moment
• Dimensions of Reynolds Number
• Dimensions of Temperature
• Dimensions of Gravitational Potential Energy
• Dimensions of Rotational Kinetic Energy

Concept of Dielectrics and Its Applications