Permittivity units and constitutive relation Assertion (A): The permittivity of free space ε0 has the dimensions of farad per metre (F/m). Reason (R): The electric flux density satisfies D = ε0 εr E, where εr is dimensionless relative permittivity and E is the electric field.

Introduction / Context:
Permittivity connects electric field E to electric flux density D. Correct unit analysis is vital in electromagnetics, dielectric design, and capacitor calculations. This item tests whether the constitutive equation explains the dimensionality of ε0.

Given Data / Assumptions:

• D = ε0 εr E in linear, isotropic media.
• εr is dimensionless; ε0 carries the physical units.
• Standard SI base units are used for dimensional analysis.

Concept / Approach:

From D = ε E in vacuum (ε = ε0), the units must satisfy [D] = [ε0][E]. Using SI, [D] = C/m^2 and [E] = V/m. Therefore [ε0] = (C/m^2) / (V/m) = C/(V·m) = F/m, because 1 F = C/V. Hence the constitutive relation directly explains the unit of ε0.

Step-by-Step Solution:

Verification / Alternative check:

Capacitance per unit length of a parallel-plate capacitor in vacuum, C = ε0 A/d, also yields [ε0] = F/m when solving for units.

Why Other Options Are Wrong:

Any option denying the equation or the dimensional derivation conflicts with standard SI definitions and Maxwell’s equations.

Common Pitfalls:

Confusing ε0 (F/m) with εr (dimensionless), or mixing Gaussian and SI unit systems.

Final Answer:

Both A and R are true and R is correct explanation of A