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The energy density in a field of 1000 V/m in free space is about

  • A.2.21 \( \mu \)J/m³
  • B.4.43 mJ/m³
  • C.4.43 \( \mu \)J/m³
  • D.8.85 \( \mu \)J/m³

Answer: C

Correct answer: 4.43 \( \mu \)J/m3

\[ u = \tfrac{1}{2}\varepsilon_0 E^2 = 0.5 \times 8.854\times10^{-12} \times 10^6 = 4.43\ \mu\mathrm{J/m^3}. \] Omitting the factor of a half gives 8.85, which is offered here - the half comes from integrating the energy as the field is built up rather than from any property of the medium.

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