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The energy stored in an electric field, per unit volume, is

  • A.\( \epsilon E^2 \)
  • B.\( \tfrac{1}{2}\epsilon E \)
  • C.\( \tfrac{1}{2}\epsilon^2 E \)
  • D.\( \tfrac{1}{2}\epsilon E^2 \)

Answer: D

It may also be written as \( \tfrac{1}{2}\mathbf{D} \cdot \mathbf{E} \), and integrating it over all space gives the same total as the pairwise sum over charges. The factor of one half arises in the same way as in the energy of a charged capacitor.

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