Dipole model of polarization in a dielectric under electric field When a homogeneous dielectric is subjected to an external electric field E, can each infinitesimal volume element be modeled as possessing an electric dipole moment (leading to a polarization vector P)?

Introduction / Context:
Macroscopic polarization is a central concept in dielectrics. It describes how bound charges in a material shift slightly under an applied electric field, producing an average dipole moment density. Modeling each differential volume as carrying a dipole helps link microscopic charge displacements to macroscopic field equations (Maxwell’s equations with polarization and bound charge densities).

Given Data / Assumptions:

• Linear, isotropic dielectric for simplicity (though the idea extends more generally).
• Small fields such that response is linear: P = ε0 χe E.
• No free charge present within the dielectric volume under consideration.

Concept / Approach:

The polarization vector P is defined as electric dipole moment per unit volume, P = dp/dV. In the continuum viewpoint, any sufficiently small volume element ΔV within a polarized medium possesses a net dipole moment p = P ΔV. This does not require permanent dipoles; even in nonpolar materials, electronic and ionic displacements create induced dipoles proportional to E. This local dipole model leads to bound charge densities ρb = −∇·P and surface bound charge σb = P·n̂ at interfaces, which correctly predict field distributions in composite dielectrics.

Step-by-Step Solution:

Verification / Alternative check:

Microscopic models (electronic/ionic/orientational polarization) average to the same macroscopic P. Measurements of capacitance and displacement current confirm the continuum description.

Why Other Options Are Wrong:

Restriction to ionic crystals or gases is unnecessary; permanent dipoles are not required for induced polarization.

Common Pitfalls:

Confusing permanent molecular dipoles with induced dipoles; both are encompassed by the macroscopic P field.

Final Answer:

True