Which expression correctly represents the electric energy density in vacuum?

Which expression correctly represents the electric energy density in vacuum?

• A. u = (1/2) ε0 E^2
• B. u = ε0 E^2
• C. u = (1/2) E^2/ε0
• D. u = (1/2) E·D

Answer: (C)

The electric energy density in a vacuum is given by u_E = (1/2) E · D. In vacuum the displacement field D equals ε0 E, so this becomes u_E = (1/2) ε0 E^2. This form correctly reflects both the factor of 1/2 and the relation between E and D in a vacuum. The alternative (1/2) E^2/ε0 would not have the right dependence on E and ε0, and ε0 E^2 would miss the 1/2 factor, giving the wrong amount of energy per volume.

The electric energy density in a vacuum is given by u_E = (1/2) E · D. In vacuum the displacement field D equals ε0 E, so this becomes u_E = (1/2) ε0 E^2. This form correctly reflects both the factor of 1/2 and the relation between E and D in a vacuum. The alternative (1/2) E^2/ε0 would not have the right dependence on E and ε0, and ε0 E^2 would miss the 1/2 factor, giving the wrong amount of energy per volume.