Which equation correctly relates D, E, and P in a dielectric?

Which equation correctly relates D, E, and P in a dielectric?

• A. D = ε0 E + P
• B. D = ε0 E
• C. D = ε E
• D. D = E + P

Answer: (B)

In dielectrics, the displacement field D captures both the electric field in space and the effect of the medium’s polarization. The fundamental relation is D = ε0 E + P. Here, ε0 E is the contribution from the vacuum part of the field, while P is the polarization—dipole moment per unit volume created when the material’s molecules align or polarize in response to the field. This shows why the polarization matters: even if the external field E is the same, a dielectric will have bound charges due to polarization, and those bound charges contribute to D through P. In a vacuum, there is no polarization, so P = 0 and D reduces to ε0 E. If a material has a linear, homogeneous response with P = ε0 χe E, then D becomes ε0 E + ε0 χe E = ε0 (1 + χe) E = ε E, where ε = ε0 εr. That’s the same idea written with the material’s permittivity ε, but the explicit form D = ε0 E + P is the clear way to show both the vacuum part and the polarization part separately. D = ε0 E would only be correct if there were no polarization (P = 0), which isn’t the case inside a dielectric. D = E + P is not dimensionally consistent, and D = ε E is a shorthand form of the same idea when you’re explicitly using the material’s permittivity. The key concept is that D combines the external field with the material’s polarization via D = ε0 E + P.

In dielectrics, the displacement field D captures both the electric field in space and the effect of the medium’s polarization. The fundamental relation is D = ε0 E + P. Here, ε0 E is the contribution from the vacuum part of the field, while P is the polarization—dipole moment per unit volume created when the material’s molecules align or polarize in response to the field.

This shows why the polarization matters: even if the external field E is the same, a dielectric will have bound charges due to polarization, and those bound charges contribute to D through P. In a vacuum, there is no polarization, so P = 0 and D reduces to ε0 E.

If a material has a linear, homogeneous response with P = ε0 χe E, then D becomes ε0 E + ε0 χe E = ε0 (1 + χe) E = ε E, where ε = ε0 εr. That’s the same idea written with the material’s permittivity ε, but the explicit form D = ε0 E + P is the clear way to show both the vacuum part and the polarization part separately.

D = ε0 E would only be correct if there were no polarization (P = 0), which isn’t the case inside a dielectric. D = E + P is not dimensionally consistent, and D = ε E is a shorthand form of the same idea when you’re explicitly using the material’s permittivity. The key concept is that D combines the external field with the material’s polarization via D = ε0 E + P.