In a dielectric, the displacement field D is related to E by D = ε E, where ε equals ε0 ε_r. Which of the following expresses this relation?

In a dielectric, the displacement field D is related to E by D = ε E, where ε equals ε0 ε_r. Which of the following expresses this relation?

• A. D = ε E
• B. D = E/ε
• C. D = ε0 E + P
• D. D = μ0 H

Answer: (A)

In a dielectric, the displacement field D scales with the electric field E through the material’s permittivity. For a linear, isotropic dielectric, this is written as D = ε E, where ε is the permittivity of the medium. Since ε = ε0 ε_r, you can also see it as D = ε0 ε_r E. This relationship comes from the fundamental definition D = ε0 E + P and, for linear dielectrics, P = χ_e ε0 E, which leads to D = ε0 (1 + χ_e) E = ε0 ε_r E. The form D = ε E directly expresses the material’s response with ε absorbing the medium’s properties, whereas D = ε0 E + P is a more general expression that depends on polarization, and D = μ0 H is a magnetic relation. D = E/ε would imply the displacement decreases as the permittivity increases, which isn’t correct for electric displacement in dielectrics.

In a dielectric, the displacement field D scales with the electric field E through the material’s permittivity. For a linear, isotropic dielectric, this is written as D = ε E, where ε is the permittivity of the medium. Since ε = ε0 ε_r, you can also see it as D = ε0 ε_r E. This relationship comes from the fundamental definition D = ε0 E + P and, for linear dielectrics, P = χ_e ε0 E, which leads to D = ε0 (1 + χ_e) E = ε0 ε_r E. The form D = ε E directly expresses the material’s response with ε absorbing the medium’s properties, whereas D = ε0 E + P is a more general expression that depends on polarization, and D = μ0 H is a magnetic relation. D = E/ε would imply the displacement decreases as the permittivity increases, which isn’t correct for electric displacement in dielectrics.