If the relative permittivity ε_r is used with ε0 to define the permittivity ε, which of the following equals ε?

If the relative permittivity ε_r is used with ε0 to define the permittivity ε, which of the following equals ε?

• A. ε = ε0
• B. ε = ε_r
• C. ε = μ0 ε_r
• D. ε = ε0 ε_r

Answer: (D)

The main idea is that a material’s ability to permit electric field lines is captured by its absolute permittivity, which scales the vacuum permittivity by the material’s relative permittivity. The relationship to use is ε = ε0 ε_r. Relative permittivity is dimensionless and describes how much the medium enhances (or diminishes) the electric response compared with vacuum. For vacuum, ε_r equals 1, so ε reduces to ε0. For most dielectrics, ε_r is greater than 1, meaning ε is larger than ε0, and the displacement field D = ε E is stronger for a given E. The product ε0 ε_r has the correct units and fully represents the medium’s electric response. Using only ε0 would describe vacuum, and including μ0 would mix magnetic properties and isn’t the correct definition.

The main idea is that a material’s ability to permit electric field lines is captured by its absolute permittivity, which scales the vacuum permittivity by the material’s relative permittivity. The relationship to use is ε = ε0 ε_r. Relative permittivity is dimensionless and describes how much the medium enhances (or diminishes) the electric response compared with vacuum. For vacuum, ε_r equals 1, so ε reduces to ε0. For most dielectrics, ε_r is greater than 1, meaning ε is larger than ε0, and the displacement field D = ε E is stronger for a given E. The product ε0 ε_r has the correct units and fully represents the medium’s electric response. Using only ε0 would describe vacuum, and including μ0 would mix magnetic properties and isn’t the correct definition.