In a linear dielectric, which expression correctly relates the displacement field D to the electric field E and the permittivity?

In a linear dielectric, which expression correctly relates the displacement field D to the electric field E and the permittivity?

• A. D = ε E
• B. D = ε0 E
• C. D = ε_r E
• D. D = E/ε

Answer: (A)

In a linear dielectric, the displacement field D is connected to the electric field E by the material’s permittivity. This comes from how polarization responds to the field: the polarization P is proportional to E, and D is defined as D = ε0 E + P. With P = χe ε0 E, you get D = ε0 (1 + χe) E = ε0 εr E, which is just another way to write D = ε E when ε represents the medium’s permittivity. Since ε = ε0 εr, the commonly used form is D = ε E. This means D = ε0 E describes the vacuum case (where εr = 1). The option D = εr E would omit the essential ε0 factor, and D = E/ε would have the wrong units and relationship. So the correct expression is D equals the medium’s permittivity times E.

In a linear dielectric, the displacement field D is connected to the electric field E by the material’s permittivity. This comes from how polarization responds to the field: the polarization P is proportional to E, and D is defined as D = ε0 E + P. With P = χe ε0 E, you get D = ε0 (1 + χe) E = ε0 εr E, which is just another way to write D = ε E when ε represents the medium’s permittivity. Since ε = ε0 εr, the commonly used form is D = ε E.

This means D = ε0 E describes the vacuum case (where εr = 1). The option D = εr E would omit the essential ε0 factor, and D = E/ε would have the wrong units and relationship. So the correct expression is D equals the medium’s permittivity times E.