Which expression correctly gives the electric energy density in vacuum?

Which expression correctly gives the electric energy density in vacuum?

• A. u_E = 1/2 ε0 E^2
• B. u_E = ε0 E^2
• C. u_E = E^2 /(2 ε0)
• D. u_E = B^2 /(2 μ0)

Answer: (B)

The electric energy density in vacuum is determined by how much energy is stored per unit volume in the electric field. The general expression for energy density is u = 1/2 E · D. In vacuum, the displacement field D equals ε0 times the electric field E, so substituting gives u_E = 1/2 ε0 E^2. This factor of 1/2 comes from integrating the work done to build up the field (it’s the work per unit volume to polarize or assemble the field). Placing ε0 in the denominator would change the dimensions, and omitting the 1/2 would double the energy density. The magnetic energy density is a different quantity, given by B^2 /(2 μ0).

The electric energy density in vacuum is determined by how much energy is stored per unit volume in the electric field. The general expression for energy density is u = 1/2 E · D. In vacuum, the displacement field D equals ε0 times the electric field E, so substituting gives u_E = 1/2 ε0 E^2. This factor of 1/2 comes from integrating the work done to build up the field (it’s the work per unit volume to polarize or assemble the field). Placing ε0 in the denominator would change the dimensions, and omitting the 1/2 would double the energy density. The magnetic energy density is a different quantity, given by B^2 /(2 μ0).