Constitutive relation and anisotropy — assertion–reason Assertion (A): The scalar relation D = ε0 εr E is applicable only to isotropic materials. Reason (R): In polycrystalline materials the directional effects are absent, so anisotropy does not occur.

Introduction / Context:This assertion–reason item checks understanding of when the simple scalar permittivity model applies and clarifies a common misconception about polycrystalline solids and anisotropy.

Given Data / Assumptions:

• Linear dielectric response.
• Possibility of anisotropy in crystals or textured materials.
• Polycrystalline aggregates may have random or non-random grain orientations.

Concept / Approach:For isotropic media, εr is a scalar and the constitutive relation is D = ε0 εr E. In anisotropic media, permittivity is a tensor ε̄, and the correct relation is D = ε̄ · E, with D generally not parallel to E. Therefore A is true. The reason R claims that polycrystalline materials lack directional effects; this is not universally true. While a fully random, statistically isotropic polycrystal may behave approximately isotropically, many polycrystals exhibit texture (preferred orientation) due to processing, retaining direction-dependent properties. Hence R is false as a general statement.

Step-by-Step Solution:Assess A → true: scalar ε applies to isotropic media only.Assess R → false: polycrystals can be anisotropic if textured; directional effects may persist.Conclusion: A true, R false.

Verification / Alternative check:Examples include rolled ferroelectric ceramics and drawn polymer films, which show anisotropic dielectric response despite being polycrystalline or semicrystalline.

Why Other Options Are Wrong:(a) and (b) assume R is true; it is not generally. (d) would negate A, which is incorrect. (e) ignores the correct part of A.

Common Pitfalls:

• Assuming “polycrystalline” automatically means “isotropic”.
• Forgetting that processing history can create texture and anisotropy.

Final Answer:A is true but R is false