In vacuum, the polarization P is zero. Which statement is correct?

In vacuum, the polarization P is zero. Which statement is correct?

• A. P = 0
• B. P = E
• C. P = D
• D. P ≠ 0 in general

Answer: (A)

Polarization is the dipole density per unit volume that a material develops when placed in an electric field. In vacuum there are no atoms or bound charges to polarize, so there is no induced dipole density at all. Therefore P = 0. This also ties into how the displacement field is defined: D = ε0 E + P. With P = 0 in vacuum, D = ε0 E, which is the same as saying the relative permittivity εr equals 1. In dielectrics, polarization is generally nonzero and related to the field by P = χe ε0 E, leading to D = εE. The statement that P ≠ 0 in general would contradict the vacuum condition, since there’s no polarizable medium in vacuum.

Polarization is the dipole density per unit volume that a material develops when placed in an electric field. In vacuum there are no atoms or bound charges to polarize, so there is no induced dipole density at all. Therefore P = 0.

This also ties into how the displacement field is defined: D = ε0 E + P. With P = 0 in vacuum, D = ε0 E, which is the same as saying the relative permittivity εr equals 1. In dielectrics, polarization is generally nonzero and related to the field by P = χe ε0 E, leading to D = εE. The statement that P ≠ 0 in general would contradict the vacuum condition, since there’s no polarizable medium in vacuum.