Polarization Relation and Definition – Assertion–Reason Assertion (A): For a linear, isotropic dielectric, the polarization vector satisfies P = ε0 * (εr − 1) * E. Reason (R): Polarization of a dielectric is defined as the dipole moment per unit volume.

Introduction / Context:
Dielectric polarization links the microscopic dipole response to the macroscopic electric field. Two statements are given: one is the constitutive relation connecting polarization to field through material constants, and the other is the basic definition of polarization. Understanding how these relate clarifies when an assertion is explained by its reason in the Assertion–Reason format.

Given Data / Assumptions:

• Linear, isotropic, homogeneous dielectric.
• Relative permittivity εr and electric susceptibility χe are related by εr = 1 + χe.
• Polarization P is a macroscopic vector field.

Concept / Approach:

The constitutive law is P = χe * ε0 * E = ε0 * (εr − 1) * E. The reason statement is a definition: polarization equals dipole moment per unit volume. While both are correct, the definition alone does not logically derive the constitutive proportionality; that proportionality follows from material linearity and isotropy assumptions (i.e., the definition plus a constitutive hypothesis). Therefore, R is true but it is not the explanation of A.

Step-by-Step Solution:

Verification / Alternative check:

In anisotropic media, P = ε0 * χ̿ * E (tensor form), showing that the constitutive law depends on material response, not the definition alone.

Why Other Options Are Wrong:

• Claiming R explains A conflates definition with constitutive behavior.
• Declaring either statement false contradicts standard electromagnetics.

Common Pitfalls:

Assuming definitions imply proportional laws; forgetting that χe encapsulates microscopic physics and must be measured or modeled.

Final Answer:

Both A and R are true but R is not the correct explanation of A