Which statement is true about the relation between D and E in vacuum and in a linear dielectric?

Which statement is true about the relation between D and E in vacuum and in a linear dielectric?

• A. True
• B. False; D = ε0 E in a dielectric
• C. False; D = E
• D. False; D = ε_r E

Answer: (A)

The key idea is how D relates to E through the medium’s permittivity. In vacuum there’s no polarization, so D = ε0 E. In a linear dielectric, polarization P is proportional to E, giving D = ε0 E + P = ε0 E + χe ε0 E = ε0 (1 + χe) E = ε0 εr E. Since ε = ε0 εr, we can also write D = ε E. So the relation is true in both cases, with the appropriate constant: ε0 in vacuum and ε0 εr (or ε) in a linear dielectric. The incorrect options either omit the ε0 factor or replace it with εr alone, which isn’t correct in SI units.

The key idea is how D relates to E through the medium’s permittivity. In vacuum there’s no polarization, so D = ε0 E. In a linear dielectric, polarization P is proportional to E, giving D = ε0 E + P = ε0 E + χe ε0 E = ε0 (1 + χe) E = ε0 εr E. Since ε = ε0 εr, we can also write D = ε E. So the relation is true in both cases, with the appropriate constant: ε0 in vacuum and ε0 εr (or ε) in a linear dielectric. The incorrect options either omit the ε0 factor or replace it with εr alone, which isn’t correct in SI units.