What is the SI unit of permittivity ε0?

What is the SI unit of permittivity ε0?

• A. N·m/C^2
• B. F/m
• C. V/m
• D. C/(N·m)

Answer: (B)

Permittivity tells how the electric field interacts with a medium, through the relation D = ε E. In vacuum this is D = ε0 E, so the units of ε0 must convert E’s units into D’s units. The electric displacement D has units of coulombs per square meter (C/m^2), while the electric field E has units of volts per meter (V/m). Therefore ε0 must have units (C/m^2) / (V/m) = C/(V·m). Since a farad is defined as C/V, ε0’s units become farads per meter (F/m). That matches the SI unit for vacuum permittivity. Numerically, ε0 ≈ 8.854×10^-12 F/m. For a quick check, in a parallel-plate capacitor the capacitance is C = ε0 A / d, which uses ε0 with units F/m, reinforcing that F/m is the correct unit.

Permittivity tells how the electric field interacts with a medium, through the relation D = ε E. In vacuum this is D = ε0 E, so the units of ε0 must convert E’s units into D’s units. The electric displacement D has units of coulombs per square meter (C/m^2), while the electric field E has units of volts per meter (V/m). Therefore ε0 must have units (C/m^2) / (V/m) = C/(V·m). Since a farad is defined as C/V, ε0’s units become farads per meter (F/m). That matches the SI unit for vacuum permittivity. Numerically, ε0 ≈ 8.854×10^-12 F/m. For a quick check, in a parallel-plate capacitor the capacitance is C = ε0 A / d, which uses ε0 with units F/m, reinforcing that F/m is the correct unit.