Question

The dipole moment per unit volume is known as

• A. Dielectric constant
• B. Polarization
• C. Capacitance
• D. Permittivity

Hint:

The unit of polarization $\vec{P}$ can be easily derived from its definition: \[ \text{Unit of } P = \frac{\text{Dipole Moment}}{\text{Volume}} = \frac{\text{Coulomb} \cdot \text{meter}}{\text{meter}^3} = \frac{\text{Coulomb}}{\text{meter}^2} \quad (\text{C/m}^2) \] Remarkably, this is identical to the units of surface charge density, reflecting the bound surface charges ($\sigma_b = \vec{P} \cdot \hat{n}$) induced at the dielectric boundaries.

Answer 1

The Correct Option is B

Concept: When an insulating or dielectric material is subjected to an external electric field, its constituent atoms or molecules undergo a structural rearrangement. The positive charges shift slightly in the direction of the field, while negative charges move in the opposite direction. This spatial separation creates induced electric dipole moments throughout the bulk of the material. To quantify this phenomenon on a macroscopic level, we define the Polarization Vector ($\vec{P}$). Let us examine the precise mathematical formulation: Suppose an elemental volume element $\Delta V$ within the dielectric contains $N$ microscopic dipoles, each possessing an individual electric dipole moment $\vec{p}_i$. The total net dipole moment within this volume is the vector sum: \[ \vec{p}_{\text{net}} = \sum_{i=1}^{N} \vec{p}_i \] The polarization $\vec{P}$ is defined as the limit of this net dipole moment per unit volume as the volume shrinks to a differential size: \[ \vec{P} = \lim_{\Delta V \to 0} \frac{\sum_{i=1}^{N} \vec{p}_i}{\Delta V} \] Hence, polarization is explicitly defined as the electric dipole moment per unit volume. Analysis of alternative parameters:
• Dielectric Constant ($\epsilon_r$): A dimensionless ratio representing the factor by which the electric field between charges is reduced relative to a vacuum. It relates the displacement field $\vec{D}$ and electric field $\vec{E}$ via $\vec{D} = \epsilon_0 \epsilon_r \vec{E}$.
• Capacitance ($C$): The structural capability of a geometric configuration of conductors to store electric charge per unit potential difference ($C = \frac{Q}{V}$), measured in Farads.
• Permittivity ($\epsilon$): An absolute material parameter that quantifies the resistance encountered when forming an electric field in a medium ($\epsilon = \epsilon_0 \epsilon_r$). Consequently, only polarization represents the dipole moment per unit volume.