Is the following statement true or false? In a linear dielectric, the energy density can also be written as u = 1/2 ε E^2.

Is the following statement true or false? In a linear dielectric, the energy density can also be written as u = 1/2 ε E^2.

• A. True
• B. False; energy density is u = 1/2 E · D
• C. False; energy density is u = 1/2 ε0 E^2
• D. False; energy density is u = 1/2 ε_r E^2

Answer: (A)

In a linear dielectric, the energy density stored in the electric field is given by u = 1/2 E · D. For an isotropic, linear dielectric, the displacement field D is proportional to E: D = ε E with ε = ε0 εr. Since E and D point in the same direction, the dot product becomes E · D = ε E^2. Plugging that in gives u = 1/2 ε E^2, which is the same as u = 1/2 ε0 εr E^2. So the statement is true. Note that u = 1/2 ε0 E^2 would only apply in vacuum, and u = 1/2 εr E^2 omits the vacuum permittivity ε0 and has the wrong units for energy density in general. The general form u = 1/2 E · D remains valid, reducing to u = 1/2 ε E^2 in a linear dielectric.

In a linear dielectric, the energy density stored in the electric field is given by u = 1/2 E · D. For an isotropic, linear dielectric, the displacement field D is proportional to E: D = ε E with ε = ε0 εr. Since E and D point in the same direction, the dot product becomes E · D = ε E^2. Plugging that in gives u = 1/2 ε E^2, which is the same as u = 1/2 ε0 εr E^2. So the statement is true.

Note that u = 1/2 ε0 E^2 would only apply in vacuum, and u = 1/2 εr E^2 omits the vacuum permittivity ε0 and has the wrong units for energy density in general. The general form u = 1/2 E · D remains valid, reducing to u = 1/2 ε E^2 in a linear dielectric.