State the energy density in a dielectric in terms of E and D.

State the energy density in a dielectric in terms of E and D.

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

Answer: (A)

The energy stored per unit volume in a dielectric is given by u = (1/2) E · D. This form comes from the work needed to assemble the field and polarization: for any electric field, the differential work is E · dD, and integrating from zero to the final D yields the half-product expression. In a linear dielectric, D = ε E, so u = (1/2) E · D = (1/2) ε E^2. In vacuum, where ε = ε0, this reduces to u = (1/2) ε0 E^2. The other expressions either ignore the material’s response (like using only E) or don't match the correct dependence on E and D, so they don’t represent the energy density in a dielectric.

The energy stored per unit volume in a dielectric is given by u = (1/2) E · D. This form comes from the work needed to assemble the field and polarization: for any electric field, the differential work is E · dD, and integrating from zero to the final D yields the half-product expression. In a linear dielectric, D = ε E, so u = (1/2) E · D = (1/2) ε E^2. In vacuum, where ε = ε0, this reduces to u = (1/2) ε0 E^2. The other expressions either ignore the material’s response (like using only E) or don't match the correct dependence on E and D, so they don’t represent the energy density in a dielectric.