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Sunlight arriving at Earth has an electric field whose rms value is 720 N/C. Determine the average total energy density of this electromagnetic radiation.

1. 4.58 × 10⁻⁶ J/m³
2. 6.37 × 10⁻⁹ J/m³
3. 81.35 × 10⁻¹² J/m³
4. 3.3 × 10⁻³ J/m³

Correct answer: 4.58 × 10⁻⁶ J/m³

Solution

For an EM wave the time-averaged total energy density equals ε0*E_rms² (the electric and magnetic parts each contribute (1/2)ε0*E_rms²). With E_rms = 720 N/C: u = 8.85×10⁻¹² × (720)² = 8.85×10⁻¹² × 5.184×10⁵ = 4.59×10⁻⁶ J/m³.

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