 # Dimensions of Dielectric Constant

## Dimensional Formula of Dielectric Constant

The dimensional formula dielectric constant is given by,

[M0 L0 IT0]

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 IT4]

∴ the dimensions of permittivity of a substance or free space = [M1 L-3 IT4]

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

Therefore, the dielectric constant is dimensionally represented as [M0 L0 IT0] = Dimensionless Quantity