Define the polarization P and the displacement D in a linear dielectric, and express D in terms of E and ε.

Define the polarization P and the displacement D in a linear dielectric, and express D in terms of E and ε.

• A. P is the dipole density; D = ε0 E + P; for a linear dielectric D = ε E with ε = ε0 ε_r; P = χ_e ε0 E.
• B. P is the polarization angle; D = E + P; for a linear dielectric D = ε0 E
• C. P is the permittivity; D = ε0 E + P
• D. P = χ_e E; D = ε0 E

Answer: (A)

Polarization density is the dipole moment per unit volume that a material develops in response to an electric field, and the displacement field D combines the external field with those bound charges. In a linear dielectric, D is defined as D = ε0 E + P. The polarization responds linearly: P = ε0 χ_e E, where χ_e is the electric susceptibility. The material’s permittivity is ε = ε0 ε_r with ε_r = 1 + χ_e, so substituting P into D gives D = ε0 E + ε0 χ_e E = ε0 (1 + χ_e) E = ε0 ε_r E = ε E. This is why the stated relations are correct: they connect P, D, E, and ε consistently for a linear dielectric.

Polarization density is the dipole moment per unit volume that a material develops in response to an electric field, and the displacement field D combines the external field with those bound charges. In a linear dielectric, D is defined as D = ε0 E + P. The polarization responds linearly: P = ε0 χ_e E, where χ_e is the electric susceptibility. The material’s permittivity is ε = ε0 ε_r with ε_r = 1 + χ_e, so substituting P into D gives D = ε0 E + ε0 χ_e E = ε0 (1 + χ_e) E = ε0 ε_r E = ε E. This is why the stated relations are correct: they connect P, D, E, and ε consistently for a linear dielectric.