Units of polarization P in SI (dipole moment per unit volume) Select the correct SI unit for dielectric polarization P (defined as electric dipole moment per unit volume).

Introduction / Context:
Polarization P quantifies the density of electric dipole moment in a dielectric. Correct units help relate P to the electric field E and electric displacement D in constitutive relations.

Given Data / Assumptions:

• P is defined as dipole moment per unit volume.
• Dipole moment p has SI units of C·m.
• Volume has SI units of m^3.

Concept / Approach:
By definition, P = (dipole moment) / (volume). Therefore, the unit is (C·m) / m^3 = C/m^2. This aligns with Maxwell’s relation D = ε0 E + P, where D has units C/m^2, ensuring dimensional consistency.

Step-by-Step Solution:
Start: unit of p = C·m.Divide by volume m^3 → C·m / m^3 = C/m^2.Confirm consistency with D and ε0 E in SI.

Verification / Alternative check:
In a linear isotropic dielectric, P = ε0(εr − 1)E, so if E is V/m and ε0 has C/(V·m), then P has C/m^2, matching the derivation.

Why Other Options Are Wrong:
“C·m” is the unit of dipole moment, not polarization. “A/m” belongs to magnetization (M). “C/m” and “V/m” do not satisfy D = ε0 E + P dimensional balance.

Common Pitfalls:

• Mixing up D (C/m^2) and E (V/m) units.
• Confusing polarization with individual dipole moment.

Final Answer:
C/m^2