Under alternating fields, is the dielectric constant (relative permittivity) a complex quantity that captures both energy storage and dielectric loss?

Introduction / Context:
In AC fields, dielectrics exhibit not only energy storage but also energy dissipation (loss). To represent both effects, engineers use a complex permittivity or complex dielectric constant, whose real part captures stored energy and whose imaginary part captures losses due to polarization lag and conduction-like behavior at the frequency of interest.

Given Data / Assumptions:

• Alternating electric field of angular frequency ω.
• Linear, time-invariant dielectric response (within small-signal regime).
• Material may have multiple polarization mechanisms with relaxation times.

Concept / Approach:

The complex dielectric constant is written as ε_r(ω) = ε′(ω) − j ε″(ω). The real part ε′ represents energy storage (capacitive behavior), while ε″ represents dielectric loss (out-of-phase response), related to dissipation factor and loss tangent tan δ = ε″/ε′. Frequency-dependent relaxation (Debye, Cole–Cole, etc.) governs how these components vary with ω.

Step-by-Step Solution:

Verification / Alternative check:

Measurement techniques (LCR meters, impedance spectroscopy) directly report ε′ and ε″ (or tan δ), confirming the complex nature over frequency.

Why Other Options Are Wrong:

• False or restricted cases: Complex permittivity is general across frequencies and material classes, not limited to optics or liquids.

Common Pitfalls:

Assuming ε is purely real; ignoring dielectric relaxation and conductivity contributions that introduce phase lag and losses.

Final Answer:

True