State the energy density of an electrostatic field in vacuum.

State the energy density of an electrostatic field in vacuum.

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

Answer: (D)

The energy stored per unit volume in an electrostatic field in vacuum scales with the square of the field strength, with a proportionality constant of one-half the vacuum permittivity. This gives u = (1/2) ε0 E^2. The reason is that energy density in fields grows with the field magnitude squared, and ε0 sets the field–energy coupling in vacuum. In vacuum, ε0 is the full permittivity, so it appears in the expression. The other forms either miss the square on the field or omit ε0, which would give incorrect units or the wrong dependence on E.

The energy stored per unit volume in an electrostatic field in vacuum scales with the square of the field strength, with a proportionality constant of one-half the vacuum permittivity. This gives u = (1/2) ε0 E^2. The reason is that energy density in fields grows with the field magnitude squared, and ε0 sets the field–energy coupling in vacuum. In vacuum, ε0 is the full permittivity, so it appears in the expression. The other forms either miss the square on the field or omit ε0, which would give incorrect units or the wrong dependence on E.