Units and dimensions of relative permittivity For the relative permittivity εr of a material (where ε = ε0 εr), what are the correct units?

Introduction / Context:
Material parameters appear in Maxwell’s equations through constitutive relations. Distinguishing absolute permittivity from relative permittivity avoids unit mistakes when calculating capacitance, wave speed, and impedance in dielectrics.

Given Data / Assumptions:

• Absolute permittivity: ε (units F/m).
• Vacuum permittivity: ε0 (units F/m).
• Relative permittivity: εr defined by ε = ε0 εr.

Concept / Approach:

Because ε and ε0 share the same units (F/m), εr must be a pure ratio and therefore dimensionless. It scales the vacuum response to represent the material’s ability to polarize relative to free space.

Step-by-Step Solution:

Verification / Alternative check:

Dielectric constant values (e.g., 2.2 for PTFE, ≈80 for water at low frequency) are quoted as plain numbers with no units, confirming εr is a ratio.

Why Other Options Are Wrong:

Options A, B, C, and E list units appropriate to ε or μ, not to the relative parameter. Only Option D correctly states “no units.”

Common Pitfalls:

Writing εr with units of F/m; mixing up ε (absolute) with εr.

Final Answer:

no units (dimensionless)