In a linear dielectric, the displacement field D relates to E by D = ε E; what is ε in terms of ε0 and κ?

In a linear dielectric, the displacement field D relates to E by D = ε E; what is ε in terms of ε0 and κ?

• A. ε = ε0 κ
• B. ε = κ / ε0
• C. ε = κ
• D. ε = ε0

Answer: (A)

In a linear dielectric, the displacement field D scales with the electric field E by D = ε E, where ε is the material’s permittivity. The permittivity of a dielectric is the vacuum permittivity ε0 multiplied by its relative permittivity κ (the dielectric constant). So ε = ε0 κ. This makes sense because ε0 has the correct units of F/m, κ is dimensionless, and multiplying by κ adjusts the field response of the material compared with vacuum. If you tried to use κ/ε0, you’d end up with incorrect units; if you used κ alone, you’d be treating ε as dimensionless; and if you used ε0 alone, you’d be assuming κ = 1 (vacuum).

In a linear dielectric, the displacement field D scales with the electric field E by D = ε E, where ε is the material’s permittivity. The permittivity of a dielectric is the vacuum permittivity ε0 multiplied by its relative permittivity κ (the dielectric constant). So ε = ε0 κ. This makes sense because ε0 has the correct units of F/m, κ is dimensionless, and multiplying by κ adjusts the field response of the material compared with vacuum.

If you tried to use κ/ε0, you’d end up with incorrect units; if you used κ alone, you’d be treating ε as dimensionless; and if you used ε0 alone, you’d be assuming κ = 1 (vacuum).