Units and dimensions: The relative permittivity (dielectric constant) εr of a material has which unit?

Introduction / Context:
Relative permittivity εr, commonly called the dielectric constant, scales a material’s absolute permittivity relative to vacuum. Correctly identifying its units helps in avoiding dimensional mistakes when using C = ε0 εr A / d or analyzing wave propagation and capacitive effects in materials.

Given Data / Assumptions:

• Absolute permittivity ε = ε0 εr.
• Vacuum permittivity ε0 has units F/m.
• εr is defined as a ratio.

Concept / Approach:

εr = ε / ε0. Since both ε and ε0 have the same units (F/m), their ratio is unitless. Thus εr is a pure number, often frequency dependent and sometimes complex under AC conditions, but dimensionless nonetheless.

Step-by-Step Solution:

Verification / Alternative check:

Datasheets list εr as a numeric value (e.g., εr ≈ 2.2 for PTFE, ≈ 80 for water at low frequency) without units.

Why Other Options Are Wrong:

• F/m or F: these are units for ε or capacitance, not εr.
• N/C and V/m: electric field-related units, not permittivity ratios.

Common Pitfalls:

Confusing absolute permittivity (ε, with units) with relative permittivity (εr, no units).

Final Answer:

Dimensionless (no units)