Properties of the relative dielectric constant (relative permittivity) Which statements about the relative dielectric constant εr are correct? It is dimensionless. It equals 1 for vacuum. It equals 1 for all substances.

Introduction / Context:
The relative dielectric constant (relative permittivity) εr quantifies how an electric field interacts with a medium compared with vacuum. It is central to capacitor design, electromagnetic wave propagation, and material characterization.

Given Data / Assumptions:

• εr is defined as ε / ε0, where ε is absolute permittivity of the material and ε0 is the permittivity of free space (vacuum).
• We consider linear, isotropic, homogeneous media under small-signal conditions.

Concept / Approach:
Because εr is a ratio of two quantities with identical units, it is dimensionless. By definition, vacuum has ε = ε0, hence εr(vacuum) = 1. Real materials differ from vacuum; most have εr > 1 (e.g., water ≈ 80 at low frequency, polymers ≈ 2–3), while some engineered metamaterials can show effective values below 1 or frequency-dispersive behavior, but not universally unity across all substances.

Step-by-Step Solution:
Check statement 1: dimensionless ratio ⇒ true.Check statement 2: ε of vacuum equals ε0 ⇒ true.Check statement 3: “equals 1 for all substances” is false; most materials deviate from unity.Therefore, the correct combination is 1 and 2 only.

Verification / Alternative check:
Standard tables list εr values for common materials; none except vacuum (and approximately dry air) have exactly 1.

Why Other Options Are Wrong:
Any option including statement 3 is incorrect; claiming “none” ignores the two correct statements.

Common Pitfalls:
Assuming air always has εr = 1 exactly; it is close to 1 but slightly greater and varies with humidity and pressure.

Final Answer:
1 and 2 only